-
Give the magnitude and direction of the net force acting on
(a) a drop of rain falling down with a constant speed,
(b) a cork of mass 10 g floating on water,
(c) a kite skilfully held stationary in the sky,
(d) a car moving with a constant velocity of 30 km/h on a rough road, [Delhi 12]
(e) a high-speed electron in space far from all gravitating objects, and free of electric and magnetic fields.
View Answer play_arrow
-
A pebble of mass 0.05 kg is thrown
vertically upwards. Give the direction and magnitude of the net force on the pebble
(i) during its upward motion.
(ii) during its downward motion.
(iii) at the highest point where
it is momentarily at rest.
Do your answers alter if the pebble were
thrown at an angle of say 45° with the horizontal direction ? Take
-
Give the magnitude and direction of the
net force acting on a stone of 0.1 kg,
(i) just after it is dropped
from the window of a stationary train.
(ii) just after it is dropped
from the window of a train running at a constant velocity of
.
(iii) just after it is dropped
from the window of a train accelerating with
.
(iv) lying on the floor of a
train which is accelerating with
the
stone being at rest relative to the train.
Neglect air resistance throughout, and
take
.
-
One end of a string of length I is
connected to a particle of mass m and the other to a small peg on a smooth
horizontal table. If the particle moves in a circle with speed v the net force on
the particle (directed towards the centre) is:
(a) T, (b)
(c)
(d)
0.
T is the tension in the string. Choose
the correct alternative.
-
A constant retarding force of 50 N is
applied to a body of mass 20 kg moving initially with a speed of. How long does
the body take to stop ?
View Answer play_arrow
-
A constant force acting on a body of
mass 3 kg changes its speed from
to
in 25 s. The
direction of motion of the force remains unchanged. What is the magnitude and
the direction of the force ?
-
A body of mass 5 kg is acted upon by two perpendicular forces of 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
View Answer play_arrow
-
The driver of a three wheeler moving
with a speed of
sees a
child standing in the middle of the road and brings his vehicle to rest in 4 s
just in time to save the child.
What is the average retarding force on
the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the
driver is 65 kg.
-
A rocket with a lift off mass 20,000 kg
is blasted upwards with an initial acceleration of
. Calculate the initial
thrust of the blast.
-
Here
.
(i) During first 10 s, the horizontal component of the velocity is
From 10 s to 11 s (i.e., for 1 s), the vertical component of the velocity is
Resultant velocity,
The direction of resultant velocity with the horizontal is given by
or
.
(ii) As there is no horizontal acceleration, the only acceleration is vertical.
Vertically downward acceleration
.
-
A bob of mass 0.1 kg hung from the
ceiling of a room by a string 2 m long is set into oscillation. The speed of
the bob at its mean position is
.
What is the trajectory of the bob if the string is cut when the bob is (a) at
one of its extreme positions, (b) at its mean position ?
-
A man weighs 70 kg. He stands on a
weighing machine in a lift, which is moving
(i) upwards with a uniform speed
of
.
(ii) downwards with a uniform
acceleration of
.
(iii) upwards with a uniform acceleration
of
.
What would be the readings on the scale
in each case ? What would be the reading, if the lift mechanism failed and it
came down freely under gravity ?
-
Fig. 5.127 shows the position-time graph
of a particle of mass 4 kg. What is the (i) force acting on the particle for
? (ii) impulse
at t = 0 and t = 4 s ?
Assume that the motion is one
dimensional.
[Delhi 09]
Fig. 5.127
-
Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) B (ii) A along the direction of string. What is the tension in the string in each case ?
View Answer play_arrow
-
Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.
View Answer play_arrow
-
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei, the products must move in opposite directions.
View Answer play_arrow
-
Two billiard balls each of mass 0.05 kg
moving in opposite directions with speed of
collide and
rebound with the same speed. What is the impulse imparted to each ball by the
other ?
-
A shell of mass 0.02 kg is fired by a
gun of mass 100 kg. If the muzzle speed of the shell
what is the recoil
speed of the gun ?
-
A batsman deflects a ball by an angle of
45° without changing its initial speed which is equal to
. What is the
impulse imparted to the ball ? Mass of the ball is 0.15 kg.
-
A stone of 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
View Answer play_arrow
-
A stone tied to the end of string is whirled round in a circle in a horizontal plane. If the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks:
(a) the stone jerks radially outwards,
(b) the stone flies off tangentially from the instant the string breaks,
(c) the stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle ?
View Answer play_arrow
-
Explain why
(a) a horse cannot pull a cart and run in empty space,
(b) passengers are thrown forward from their seats when a speeding bus stops suddenly,
(c) it is easier to pull a lawn mower than to push it,
(d) a cricketer moves his hands backwards while holding a catch.
View Answer play_arrow
-
Fig. 5.131 below shows the position-time
graph of a particle of mass 0.04 kg. Suggest a suitable physical context for
this motion. What is the time between two consecutive impulses received by the
particle ? What is the magnitude of each impulse ?
-
Fig. 5.132 shows a man standing
stationary with respect to a horizontal conveyor belt that is accelerating with
. What is the
net force on the man ? If the coefficient of static friction between the man's
shoes and the belt is 0.2, up to what acceleration of the belt can the man
continue to be stationary relative to the belt ? Mass of the man = 65 kg.
Fig. 5.132
-
View Answer play_arrow
-
A helicopter of mass 1000 kg rises with
a vertical acceleration of
.
The crew and the passengers weigh 300 kg. Give the magnitude and direction of
(i) force on the floor by the
crew and passengers.
(ii) action of the rotor of the
helicopter on the surrounding air.
(iii) force on the helicopter
due to the surrounding air.
Take
[Delhi
03]
-
A stream of water flowing horizontally
with a speed of
gushes
out of a tube of cross-sectional area
and hits at a
vertical wall nearby. What is the force exerted on the wall by the impact of
water, assuming it does not rebound ?
-
Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m kg. Give the magnitude and direction of
(i) the force on the 7th coin (counted from the bottom) due to all the coins on its top.
(ii) the force on the 7th coin by the eighth coin.
(iii) the reaction of the 6th coin on the 7th coin.
View Answer play_arrow
-
An aircraft executes a horizontal loop
at a speed of
with
its wings banked at 15°. What is the radius of the loop
?
-
A train runs along an unbanked circular
track of radius 30 mat a speed of
.
The mass of the train is
.
What provides the centripetal force required for this purpose ? The engine or
the rails ? The outer or the inner rail ?
Which rail will wear out faster,
the outer or the inner rail ?
What is the angle of banking required to
prevent wearing out of the rails ?
-
A block of mass 25 kg is raised by a 50
kg man in two different ways as shown in Fig. 5.133. What is the action on the floor
by the man in the two cases ? If the floor yields to a normal force of 700 N,
which mode should the man adopt to lift the block without the floor yielding ?
(a) (b)
Fig. 5.133
-
A monkey of mass 40 kg climbes on a rope
which can stand a maximum tension of 600 N [Fig. 5.134]. In which of the following
cases will the rope break : the monkey
(i) climbs up with an
acceleration of
(ii) climbs down with an
acceleration of
(iii) climbs up with a uniform
speed of
(iv) falls down the rope nearly freely
under gravity ?
Take
. Ignore the
mass of the rope.
Fig. 5.134 Fig.
5.135
-
Two bodies A and B of masses 5 kg and
10kg in contact with each other rest on a table against a rigid partition.
The coefficient of friction
between the bodies and the table is 0.15. A force of 200 N is applied
horizontally at A. What are
(i) the reaction of the
partition (ii) the action-reaction forces between A and B ? What happens when
the partition is removed ?
Does answers to (ii) change/when
the bodies are in motion ?
Ignore difference between
and
.
-
A block of mass 15 kg is placed on a long
trolley. The coefficient of friction between the block and the trolley is 0.18.
The trolley accelerates from rest with
for 20 s and
then moves with uniform velocity. Discuss the motion of the block as viewed by
(i) a stationary observer on the ground (ii) an observer moving with the
trolley.
-
The rear side of a truck is open and a
box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.137.
The coefficient of friction
between the box and the surface below it is 0.15. On a straight road, the truck
starts from rest and accelerates with
. At what
distance from the starting point does the box fall off the truck ? Ignore the
mass of the box.
Fig. 5.137
-
The rear side of a truck is open and a
box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.137.
The coefficient of friction
between the box and the surface below it is 0.15. On a straight road, the truck
starts from rest and accelerates with
. At what
distance from the starting point does the box fall off the truck ? Ignore the
mass of the box.
Fig. 5.137
-
A disc revolves with a speed of
and has a
radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of
the disc. If the coefficient of friction between the coins and the disc is
0.15, which of the two coins will revolve with the disc? Take
.
-
You may have seen in a circus a motorcyclist driving in vertical loops inside a 'death-well' (a hollow spherical chamber with holes, so that the spectators can watch from outside).
Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required to perform a vertical loop if the radius of the chamber is 25m?
View Answer play_arrow
-
A 70 kg man stands in contact against
the wall of a cylindrical drum of radius 3 m rotating about its vertical axis with
. The
coefficient of friction between the wall and his clothing is 0.15. What is the
minimum rotational speed if the cylinder to enable the man to remain stuck to
the wall (without falling) when the floor is suddenly removed ?
-
A thin circular loop of radius R rotates
about its vertical diameter with an angular frequency
. Show that a small
bead on the wire remains at its lowermost point for
. What is the
angle made by the radius vector joining the centre to the bead with the
vertical downward direction for
?
Neglect friction.
-
question_answer41)
A
ball is travelling with uniform translatory motion. This means that
(a)
it is at rest.
(b)
the path can be a straight line or circular and the ball travels with uniform
speed.
(c)
all parts of the ball have the same velocity (magnitude and direction) and the
velocity is constant.
(d)
the centre of the ball moves with constant velocity and the ball spins about
its centre uniformly.
View Answer play_arrow
-
question_answer42)
A
metre scale is moving with uniform velocity. This implies
(a)
the force acting on the scale is zero, but a torque about die centre of mass
can act on the scale.
(b)
the force acting on the scale is zero and the torque acting about centre of
mass of the scale is also zero.
(c)
the total force acting on it need not be zero but the torque on it is zero
(a)
neither the force nor the torque need to be zero.
View Answer play_arrow
-
question_answer43)
A
cricket ball of mass 150 g has an initial velocity \[\vec{u}=\,(3\hat{i}+\,4\hat{j})\,m{{s}^{-1}}\]
and a final
velocity \[\vec{u}=(3\hat{i}\,\,+\,4\hat{i})\,m{{s}^{-1}}\] and a final
velocity \[\vec{v}=\,-(3\hat{i}\,\,+\,4\hat{i})\,m{{s}^{-1}}\] after being hit.
The change in momentum (final momentum initial momentum) is (in kg \[m{{s}^{-1}}\]1)
(a)
zero (b) \[-\,(0.45\hat{i}\,+\,0.6\hat{j})\]
(c)
\[-\,(0.9\hat{i}\,+1.2\hat{j})\] (d) \[-5\,(\hat{i}+\,\hat{j})\]
View Answer play_arrow
-
question_answer44)
In
the previous problem (3), the magnitude of the momentum transferred during the
hit is
(a)
Zero (b) \[0.75\text{ }kg\text{
}m{{s}^{1}}\]
(c) \[1.5\text{
}kg\text{ }m{{s}^{1}}\] (d) \[14\text{ }kg\text{ }m{{s}^{1}}\]
View Answer play_arrow
-
question_answer45)
Conservation
of momentum in a collision between particles call be understood from
(a)
Conservation of energy.
(b)
Newton's first law only.
(c)
Newton's second law only.
(d)
both Newton's second and third law.
View Answer play_arrow
-
question_answer46)
A
hockey player is moving northward and suddenly turns westward with the same
speed to avoid all opponent. The force that acts on the player is
(a)
frictional force along westward.
(b)
muscle force along southward.
(c)
frictional force along south-west.
(d)
muscle force along south-west.
View Answer play_arrow
-
question_answer47)
A
body of mass 2kg travels according to the law
\[x(t)=pt+q{{t}^{2}}+r{{t}^{3}}\]
where \[p=3\,m{{s}^{-1}},\,q=4\,m{{s}^{-2}}\]and
\[r=5\text{ }m{{s}^{3.}}\]
The
force acting on the body at \[t=2\] seconds is
(a)
136 N (b)) 134 N
(c)
15 8 N (d) 68 N
View Answer play_arrow
-
question_answer48)
A
body with mass 5 kg is acted upon by a force
\[\vec{F}\,=(-3\hat{i}\,+\,4\hat{j})\,\,N\].
If its initial velocity at \[t=0\] is \[\vec{\upsilon
}=(6\hat{i}-12\hat{j})\,\,m{{s}^{-1}}\], the time at which it will just have a
velocity along the y-axis is
(a)
never (b) 10 s
(c)
2 s (d) 15 s
View Answer play_arrow
-
question_answer49)
A
car mass m starts from rest and acquires a velocity along east \[\vec{\upsilon
}=v\hat{i}\,\,(\upsilon >\,O)\] in two seconds. Assuming the car moves with
uniform acceleration, the force exerted on the car is
(a)
\[\frac{m\upsilon }{2}\] eastward and is exerted by the car engine.
(b)
\[\frac{m\upsilon }{2}\] eastward and is due to the friction on the typres
exerted by the road.
(c)
more than \[\frac{m\upsilon }{2}\] eastward exerted due to the engine and
overcomes the friction of the road.
(d)
\[\frac{m\upsilon }{2}\]exerted by the engine.
View Answer play_arrow
-
question_answer50)
The
motion of a particle of mass m is given by \[x=0\] for \[t<0\text{
}s,\text{ }x(t)=A\text{ }\sin \text{ }4\pi \,t\] for \[0<t<(1/4)s\text{
}(A>o),\] and
\[x=0\] for
\[t>(1/4)s\]. Which of the following statements is true?
(a)
The force at \[t=(1/8)s\] s on the particle is \[-16{{\pi }^{2}}\,A\,m\] .
(b)
The particle is acted upon by an impulse of magnitude \[4\,{{\pi }^{2}}\,A\,m\]
at \[t=0\,s\] and\[t=(1/4)s\] .
(c)
The particle is not acted upon by any force.
(d)
The particle is not acted upon by a constant force.
(e)
There is no impulse acting on the particle.
View Answer play_arrow
-
question_answer51)
In
Fig. the co-efficient of friction between the floor and the body B is 0.1. The
coefficient of friction between the bodies B and A is 0.2. A force F is applied
as shown on B. The mass of A is m/2 and of B is m. Which of the following
statements are true?
(a)
The bodies will move together if \[F=0.25\,mg\].
(b)
The body A will slip with respect to B if F = \[F=0.5\,mg\].
(c)
The bodies will move together if \[F=0.5\,mg\]
(d)
The bodies will be at rest if \[F=0.1\,mg\]
(e)
The maximum value of F for which the two bodies will move together is \[0.45\,\,\,mg\].
View Answer play_arrow
-
question_answer52)
Mass
\[{{m}_{1}}\] moves on a slope making an angle with the horizontal and is
attached to mass \[{{m}_{2}}\] by a string passing over a frictionless pulley
as shown in Fig. The co-efficient of friction between nil and the sloping
surface is \[\mu \] .
Which
of the following statements are true?
(a)
If \[{{m}_{2}}>{{m}_{1}}\sin \,\theta ,\] the body will move up the plane.
(b)
If \[{{m}_{2}}>{{m}_{1}}(\sin \,\theta +\mu \cos \theta ),\] the body will move
up the plane.
(c)
If \[{{m}_{2}}<{{m}_{1}}(\sin \,\theta +\mu \cos \theta ),\] the body will move
up the plane.
(d)
If \[{{m}_{2}}<{{m}_{1}}(\sin \,\theta -\mu \cos \theta ),\] the body will move
down the plane.
View Answer play_arrow
-
question_answer53)
In
Fig. a body A of mass \[m\] slides on plane inclined at angle \[{{\theta }_{1}}\]
to the
horizontal and \[{{\mu }_{1}}\] is the coefficient of friction between A
and the plane. A is connected by a light string passing over a frictionless
pulley to another body B, also of mass \[m,\] sliding on a frictionless plane
inclined at angle \[{{\theta }_{2}}\] to the horizontal. Which of the following
statement are true?
(a)
A will never move up the plane.
(b)
A will just start moving up the plane when
\[\mu
=\,\frac{\sin \,{{\theta }_{2}}\,-\,\sin \,{{\theta }_{1}}}{\cos {{\theta
}_{1}}}\]
(c)
For A to move up the plane, \[{{\theta }_{2}}\] must always be greater than \[{{\theta
}_{1}}\].
(d)
B will always slide down with constant speed.
View Answer play_arrow
-
question_answer54)
Two
billiard balls A and B, each of mass 50g and moving, in opposite directions with
speed of \[5\,m{{s}^{-1}}\] each, collide and rebound with the same speed. If the
collision lasts for \[{{10}^{-3}}\,s,\] which of the following statements are true?
(a)
The impulse imparted to each ball is \[0.25\,\,kg\,\,m{{s}^{-1}}\] and the force oil
each ball is 250 N.
(b)
The impulse imparted to each ball is \[0.25\,\,kg\,\,m{{s}^{-1}}\] and the force
exerted on each ball is \[25\times {{10}^{5}}N\].
(c)
The impulse imparted to each ball is 0.5 Ns.
(d)
The impulse and the force oil each ball are equal in magnitude and opposite in
direction.
View Answer play_arrow
-
question_answer55)
A
body of mass l0kg is acted upon by two perpendicular forces, 6N and 8N. The
resultant acceleration of the body is
(a)
\[1\text{ }m\text{ }{{s}^{2}}\] at an angle of \[{{\tan }^{1}}\left(
\frac{4}{3} \right)\] w.r.t.
6 N force.
(b)
\[0.2\text{ }m\text{ }{{s}^{-2}}\] at an angle of \[{{\tan }^{1}}\left(
\frac{4}{3} \right)\] w.r.t.
r. 6 N force.
(c)
\[1\text{ }m{{\text{s}}^{-2}}\] at an angle of \[{{\tan }^{-1}}\left(
\frac{3}{4} \right)\] w.r.t.
8 N force.
(d)
\[0.2\text{ }m{{s}^{2}}\] at an angle of \[{{\tan }^{1}}\left( \frac{3}{4}
\right)\] w.r.t
8 N force.
View Answer play_arrow
-
question_answer56)
A
girl riding a bicycle along a straight road with a speed of \[5\text{
}m{{s}^{1}}\] throws a stone of mass 0.5 kg which has a speed of \[15\text{
}m{{s}^{1}}\] with
respect to the ground along her direction of motion. The mass of the girl and
bicycle is 50 kg. Does the speed of the bicycle change after the stone is
thrown? What is the change in speed, if so?
View Answer play_arrow
-
question_answer57)
A person of mass 50
kg stands oil a weighing scale oil a lift. If die lift is descending with a
downward acceleration of \[9\,m\,{{s}^{-2}}\], what would be the reading of the
weighing scale? \[(g=10\,m\,{{s}^{-2}})\]
View Answer play_arrow
-
question_answer58)
The position time
graph of a body of mass 2 kg is as given in Fig. What is the impulse on die
body at \[t=0\,s\] and
\[t=4\,s\].
View Answer play_arrow
-
question_answer59)
A
person driving a car suddenly applies the brakes on seeing a child oil the road
ahead. If lie is not wearing seat belt, he falls forward and hits his head
against the steering wheel. Why?
View Answer play_arrow
-
question_answer60)
The
velocity of a body of mass 2 kg as a function of t is given by \[v(t)=2t\,\hat{i}+{{t}^{2}}\,\hat{j}\].
Find the momentum and the force acting on it, at time \[t=\,2s\].
View Answer play_arrow
-
question_answer61)
A
block placed oil a rough horizontal surface is pulled by a horizontal force F.
Let f be the force applied by the rough surface on the block. Plot a
graph off versus F.
View Answer play_arrow
-
question_answer62)
Why
are porcelain objects wrapped in paper or straw before packing for
transportation?
View Answer play_arrow
-
question_answer63)
Why does a child
feel more pain when she falls down oil a hard cement floor, than when she falls
oil the soft muddy ground in the garden?
View Answer play_arrow
-
question_answer64)
A
woman throws all object of mass 500 g with a speed of \[25\,m{{s}^{-1}}\] .
(a)
What is the impulse imparted to the object?
(b)
If the object hits a wall and rebounds with half the original speed, what is
the change in momentum of the object?
View Answer play_arrow
-
question_answer65)
Why
are mountain roads generally made winding upwards rather than going straight
up?
View Answer play_arrow
-
question_answer66)
A
mass of 2kg is suspended with thread AB (Fig.). Thread CD of the same type is
attached to the other end of 2 kg mass. Lower thread is pulled gradually,
harder and harder in the downward director so as to apply force on AB. Which of
the threads will break and why?
View Answer play_arrow
-
question_answer67)
In
the above given problem if the lower thread is pulled with a jerk, what
happens?
View Answer play_arrow
-
question_answer68)
Two
masses of 5 kg and 3 kg are suspended with help of massless inextensible
strings as shown in Fig. Calculate \[{{T}_{1}}\] and \[{{T}_{2}}\] when whole
system is going upwards with acceleration \[=2\,m{{s}^{-2}}\] (use \[g=9.8\,m\,{{s}^{-2}}\]).
View Answer play_arrow
-
question_answer69)
Block
A of weight 100 N rests on a frictionless inclined plane of slope angle \[{{30}^{o}}\]
(Fig.). A
flexible cord attached to A passes over a frictonless pulley and is connected
to block B of weight W. Find the weight W for which the system is in
equilibrium.
View Answer play_arrow
-
question_answer70)
A block
of mass M is held against a rough vertical wall by pressing it with a finger.
If the coefficient of friction between the block and the wall is \[\mu \]
and the
acceleration due to gravity is g, calculate the minimum force required to be
applied by the finger to hold the block against the wall?
View Answer play_arrow
-
question_answer71)
A
100 kg gun fires a ball of 1kg horizontally from a cliff of height 500m. It
falls on the ground at a distance of 400m from the bottom of the cliff. Find
the recoil velocity of the gun. (Acceleration due to gravity \[=10\,m{{s}^{-2}}\])
View Answer play_arrow
-
question_answer72)
Figure
shows \[(x,\,t),\,(y,\,t)\] diagram of a particle moving in 2-dimensions.
If
the particle has a mass of 500 g, find the force (direction and magnitude)
acting on the particle.
View Answer play_arrow
-
question_answer73)
A
person in all elevator accelerating upwards with all acceleration of \[2\,\,m{{s}^{-2}}\],
tosses a coin vertically upwards with a speed of \[20\,\,m{{s}^{-1}}\]. After how
much time will the coin fall back into his hand ? \[(g=10\,\,m{{s}^{-2}})\]
View Answer play_arrow
-
question_answer74)
There
are three forces \[{{F}_{1}},\,{{F}_{2}}\] and \[{{F}_{3}}\] acting on a body,
all acting on a point P on the body. The body is found to move with uniform
speed.
(a)
Show that the forces are coplanar.
(b)
Show that the torque acting on the body about any point due to these three
forces is zero.
View Answer play_arrow
-
question_answer75)
When
a body slides down from rest along a smooth inclined plane making an angle of
45 0 with the horizontal, it takes time T. When die same body slides down from
rest along a rough inclined plane making the same angle and through die same
distance, it is seen to take time pT, where p is some number greater than 1.
Calculate the coefficient of friction between the body and the rough plane.
View Answer play_arrow
-
question_answer76)
Figure
shows \[({{\upsilon }_{x}},\,t),\] and \[({{\upsilon }_{y}},\,t)\] diagrams for a body
of unit mass. Find the force a function of time.
View Answer play_arrow
-
question_answer77)
A
racing car travels on a track (without banking) ABCDEFA (Fig.) ABC is a
circular arc of radius 2R. CD and FA are straight paths of length R and DEF is
a circular arc of radius R = 100 m. The co-efficient of friction on the road is
\[\mu =\,0.1\]. The maximum speed of the car is \[50\,m\,{{s}^{-1}}\]. Find the
minimum time for completing one round.
View Answer play_arrow
-
question_answer78)
The
displacement vector of a particle of mass m is given by \[r(t)=\hat{i}\,\,A\,\,\cos
\,\omega t+\hat{j}B\,\sin \omega t\].
(a)
Show that the trajectory is an ellipse.
(b)Show
that \[F=-\,m{{\omega }^{2}}r\].
View Answer play_arrow
-
question_answer79)
A
cricket bowler releases the ball in two different ways
(a)
giving it only horizontal velocity, and
(b)
giving it horizontal velocity and a small downward velocity.
The
speed \[{{\upsilon }_{s}}\] at the time of release is die same. Both are released
at a height H from the ground. Which one will have greater speed when the ball
hits, the ground? Neglect air resistance.
View Answer play_arrow
-
question_answer80)
There
are four forces acting at a point P produced by strings as shown in Fig. which
is at rest. Find the forces \[{{F}_{1}}\] and \[{{F}_{2}}\].
View Answer play_arrow
-
question_answer81)
A
rectangular box lies on a rough incline surface. The co-efficient of friction
between the surface and the box is \[\mu \]. Let the mass of the box be m.
(a)
At what angle of inclination \[\theta \] of the plane to the horizontal will the box
just start to slide down the plane?
(b)
What is the force acting oil the box down the plane, if the angle of
inclination the plane is increased to \[a>0\]?
(c)
What is the force needed to be applied upwards along the plane to make the box
either remain stationary or just move up with uniform speed?
(d)
What is the force needed to be applied upwards along the plane to make the box move
up the plane with acceleration a?
View Answer play_arrow
-
question_answer82)
A
helicopter of mass 2000 kg rises with a vertical acceleration of \[15\,m{{s}^{-2}}\].
The total mass of the crew and passengers is 500 kg. Give the magnitude and
direction of the \[(g=10\,m{{s}^{-2}})\]
(a)
force oil the floor of the helicopter by the crew and passengers.
(b)
action of die rotor of the helicopter on the surrounding air.
(c)
force oil the helicopter due to the surrounding air.
View Answer play_arrow
(ii)
(iii)
(iv)
(and 
) denote the
tension in the string (and the speed of the stone) at the lowest and the
highest point respectively. Choose the correct alternative.
