question_answer2) The minimum velocity (in \[m{{s}^{-1}}\]) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction \[0.6\] to avoid skidding is [AIEEE 2002]
question_answer3) A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively [AIEEE 2002]
question_answer4) When forces \[{{F}_{1}},{{F}_{2}},{{F}_{3}}\] are acting on a particle of mass m such that \[{{F}_{1}}\] and \[{{F}_{2}}\] are mutually perpendicular, then the particle remains stationary. If the force \[{{F}_{1}}\] is now removed, then the acceleration of the particle is [AIEEE 2002]
question_answer5) Speeds of two identical cars are u and 4 u at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is [AIEEE 2002]
Three identical blocks of masses \[m=2\] kg are drawn by a force \[F=10.2\] N with an acceleration of \[0.6\,\,m{{s}^{-2}}\] on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C? [AIEEE 2002]
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in \[m{{s}^{-2}}\]) can a man of 60 kg climb on the rope? [AIEEE 2002]
question_answer8) A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of \[5\,m/{{s}^{2}}\], the reading of the spring balance will be [AIEEE 2003]
Three forces start acting C simultaneously on a particle moving with velocity v. These forces are represented in magnitude and direction by the three sides of a \[\Delta ABC\] (as shown). The particle will now move with velocity
[AIEEE 2003]
A)
less than v
doneclear
B)
greater than v
doneclear
C)
\[\left| v \right|\] in the direction of largest force BC
A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \[0.2\]. The weight of the block is [AIEEE 2003]
question_answer11) A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then, the coefficient of friction is [AIEEE 2003]
question_answer12) A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is [AIEEE 2003]
question_answer13) A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then, the true statement about the scale reading is [AIEEE 2003]
A)
both the scales read M kg each
doneclear
B)
the scale of the lower one reads M kg and of the upper one zero
doneclear
C)
the reading of the two scales can be anything but the sum of the readings will be M kg '
question_answer14) A rocket with a lift-off mass \[3.5\times {{10}^{4}}\] kg is blasted upwards with an initial acceleration of \[10\,m/{{s}^{2}}\] . Then, the initial thrust of the blast is [AIEEE 2003]
question_answer16) A machine gun fires a bullet of mass 40 g with a velocity\[1200\text{ }m{{s}^{-1}}\]. The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most? [AIEEE 2004]
Two masses\[{{m}_{1}}=5\,kg\]and\[{{m}_{2}}=4.8\,kg\]lied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move? [AIEEE 2004]
question_answer18) A block rests on a rough inclined plane making an angle of\[30{}^\circ \]with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take\[g=10\text{ }m/{{s}^{2}}\]) [AIEEE 2004]
question_answer19) A force\[F=(5\hat{i}+3\hat{j}+2\hat{k})\] is applied over a particle which displaces it from its origin to the point\[r=(2\hat{i}-\hat{j})m\]. The work done on the particle in joules is [AIEEE 2004]
question_answer20) A smooth block is released at rest on a\[45{}^\circ \]incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is [AIEEE 2005]
question_answer21) The upper half of an inclined plane with inclination\[\phi \]is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by [AIEEE 2005]
A block is kept on a frictionless inclined surface with angle of inclination a. The incline is given an acceleration a to keep the block stationary. Then, a is equal to [AIEEE 2005]
question_answer23) A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass\[\frac{1}{3}\]M and a body C of mass\[\frac{2}{3}\]M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards [AIEEE 2005]
question_answer24) A particle of mass 0.3 kg is subjected to a force \[F=-\text{ }kx\]with\[k=15\text{ }N/m.\]What will be its initial acceleration, if it is released from a point 20 cm away from the origin? [AIEEE 2005]
question_answer25) Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped, is\[[{{\mu }_{k}}=0.5]\] [AIEEE 2005]
question_answer26) A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is\[4\text{ }m{{s}^{-1}}\]. The kinetic energy of the other mass is [AIEEE 2006]
question_answer27) A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. If the catching process is completed in 0.1 s, the force of the blow exerted by the ball on the hand of the player is equal to [AIEEE 2006]
question_answer28) A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and' the spring is upstretched.Then, a constant force F starts acting on the block of mass M to pull it; Find the force on the block of mass m. [AIEEE 2007]
The figure shows the position - time (x - t) graph of one-dimensional motion of the body of mass 0.4 kg. The magnitude of each impulse is [AIEEE 2010]
question_answer30) For a particle in uniform circular motion, the acceleration\[\overrightarrow{a}\]at a point\[P(R,\text{ }\theta )\]on the circle of radius R is (Here\[\theta \]is measured from the x-axis) [AIEEE 2010]
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out a length\[s={{t}^{3}}+5,\]where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of P when\[t=2s\] is nearly. [AIEEE 2010]
question_answer32) The minimum force required to start pushing a body up a rough (frictional coefficient \[\mu \]) inclined plane is \[{{F}_{1}}\] while the minimum force needed to prevent it from sliding down is \[{{F}_{2}}.\] If the inclined plane makes an angle \[\theta \]from the horizontal such that \[\tan \theta =2\mu \]then the ratio \[\frac{{{F}_{1}}}{{{F}_{2}}}\] is : [AIEEE 11-05-2011]
question_answer33) If a spring of stiffness 'k' is cut into two parts 'A' and 'B' of length \[{{\ell }_{A}}:{{\ell }_{B}}=2:3,\]then the stiffness of spring 'A' is given by: [AIEEE 11-05-2011]
question_answer34) A particle of mass m is at rest at the origin at time\[t=0\]. It is subjected to a force \[F(t)={{F}_{0}}{{e}^{-bt}}\] in the \[x\] direction. Its speed v(t) is depicted by which of the following curves? [AIEEE 2012]
question_answer35) Two cars of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are moving in circles of radii \[{{r}_{1}}\] and \[{{r}_{2}}\], respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is: [AIEEE 2012]
question_answer36) A car of mass 1000 kg is moving at a speed of 30 m/s. Brakes are applied to bring the car to rest. If the net retarding force is 5000 N, the car comes to stop after travelling dm in t s. Then [JEE ONLINE 07-05-2012]
A projectile moving vertically upwards with a velocity of 200 \[\text{m}{{\text{s}}^{-1}}\]breaks into two equal parts at a height of 490 m. One part starts moving vertically upwards with a velocity of 400 \[\text{m}{{\text{s}}^{-1}}\]. [JEE ONLINE 12-05-2012]
How much time it will take, after the break up with the other part to hit the ground?
An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of a so that the insect does not slip is given by [JEE ONLINE 12-05-2012]
question_answer39) Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of 3 \[\text{m}{{\text{s}}^{\text{-1}}}\]will be [JEE ONLINE 19-05-2012]
question_answer40) A block of weight crests on a horizontal floor with coefficient of static friction \[\mu .\]It is desired to make the block move by applying minimum amount offered. The angle \[\theta \] from the horizontal at which the force should be applied and magnitude of the force F are respectively. [JEE ONLINE 19-05-2012]
question_answer41) A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of\[\frac{dM}{dt}=\alpha v\] where M is the mass (of satellite dt + dust) at that instant. The instantaneous acceleration of the satellite is [JEE ONLINE 26-05-2012]
A uniform sphere of weight W and radius 5cm is being held by a string as shown in the figure. The tension in the string will be: [JEE ONLINE 09-04-2013]
Two blocks of mass \[{{M}_{1}}=20\,kg\] and \[{{\operatorname{M}}_{2}}=12\operatorname{K}\operatorname{g},\] are connected by a metal rod of mass 8 kg. The system is pulled vertically up applying a force of 480 N as shown. The tension at mid-point of the rod is:
question_answer45) A body stars from rest on a long inclined plane of slope \[{{45}^{o}}\]. The coefficient of friction between the body and the plane varies as \[\mu =0.3\,x,\] where \[x\] is distance travelled down the down the plane. The body will have maximum speed (for g=10 m/\[{{\text{s}}^{\text{2}}}\]) when \[x\]= : [JEE ONLINE 22-04-2013]
A mass m = 1.0kg is put on a flat pan attached to vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan? [JEE ONLINE 22-04-2013]
(Take g = 10 m/\[{{\operatorname{s}}^{2}}\]).
The spring is stiff enough so that it does not get distorted during the motion.
question_answer47) A projectile of mass M is fired so that the horizontal range is 4 km At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part states falling down vertically with zero initial speed. The horizontal range (distance from point of firing of the lighter part is): [JEE ONLINE 23-04-2013]
question_answer48) A body of mass m is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm. If the angular velocity is doubled, elongation in the spring is 5 cm. The original length of the spring is: [JEE ONLINE 23-04-2013]
question_answer49) A block is paced on a rough horizontal plane. A time dependent horizontal force \[\operatorname{F}=\operatorname{Kt}\] acts on the block, where k is a positive constant. The acceleration time graph of the block is: [JEE ONLINE 25-04-2013]
question_answer50) A block of mass m is placed on a surface with a vertical cross section given by \[y=\frac{{{x}^{3}}}{6}.\]If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is: [JEE MAIN 2014]
question_answer51) A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied to B for the blocks to move together will be: [JEE ONLINE 09-04-2014]
A small ball of mass m starts at a point A with speed \[{{v}_{0}}\] and moves along a frictionless track AB as shown. The track BC has coefficient of friction m. The ball comes to stop at C after travelling a distance L which is:
question_answer53) A bullet of mass 4g is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately? [JEE ONLINE 12-04-2014]
A heavy box is to dragged along a rough horizontal floor.
To do so, person A pushes it at an angle 30° from the horizontal and requires a minimum force \[{{F}_{A}},\] while person B pulls the box at an angle 60° from the horizontal and needs minimum force FB. If the coefficient of friction between the box and the floor is \[\frac{\sqrt{3}}{5},\]the ratio \[\frac{{{F}_{A}}}{{{F}_{B}}}\]is [JEE ONLINE 19-04-2014]
Given in the figure are two blocks A and B of weight 20 N and 100N respectively. There are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is: [JEE MAIN 2015]
question_answer56) If a body moving in a circular path maintains constant speed of\[\frac{3}{2}ma\], then which of the following correctly describes relation between acceleration and radius? [JEE ONLINE 10-04-2015]
question_answer57) A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle\[\theta \]. With the horizontal, a point object of mass m is kept. The minimum coefficient of friction \[{{\mu }_{\min }}\] between the mass and the inclined surface such that he mass does not move is: [JEE ONLINE 09-04-2016]
question_answer58) A particle of mass m is acted upon by a force F given by the empirical law \[F=\frac{R}{{{t}^{2}}}V(t)\].If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot: [JEE ONLINE 10-04-2016]
A conical pendulum of length 1 m makes an angle \[\theta ={{45}^{\text{o}}}\] w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be - (Take \[g=10\,m{{s}^{-1}}\]) [JEE Online 09-04-2017]
question_answer60) The mass of a hydrogen molecule is \[3.32\times {{10}^{-27}}kg\]. If \[{{10}^{23}}\] hydrogen molecules strike, per second, a fixed wall of area \[\text{2 c}{{\text{m}}^{\text{2}}}\] at an angle of \[\text{45 }\!\!{}^\circ\!\!\text{ }\] to the normal, and rebound elastically with a speed of \[\text{1}{{\text{0}}^{\text{3}}}\text{ m/s}\], then the pressure on the wall is nearly: [JEE Main Online 08-04-2018]
Two masses \[{{m}_{1}}=5kg\] and \[{{m}_{2}}=10kg\], connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of \[{{m}_{2}}\] to stop the motion is : [JEE Main Online 08-04-2018]
question_answer62) A given object takes \[n\] times more time to slide down a \[45{}^\circ \] rough inclined plane as it takes to slide down a perfectly smooth \[45{}^\circ \] incline. The coefficient of kinetic friction between the object and the incline is : [JEE Online 15-04-2018]
question_answer63) An automobile, travelling at \[40km/h\], can be stopped at a distance of \[40m\]by applying brakes. If the same automobile is travelling at \[80km/h\], the minimum stopping distance, in metres, is (assume no skidding) [JEE Online 15-04-2018]
question_answer64) A body of mass \[2kg\] slides down with an acceleration of \[3m/{{s}^{2}}\] on a rough inclined plane having a slope of \[30{}^\circ \]. The external force required to take the same body up the plane with the same acceleration will be:\[(g=10m/{{s}^{2}})\][JEE Online 15-04-2018 (II)]
question_answer65) A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is\[(g=10m/{{s}^{2}})\][JEE Online 15-04-2018 (II)]
question_answer66) Two particles of the same mass m are moving in circular orbits because of force, given by \[F(r)=\frac{-16}{r}-{{r}^{3}}\]The first particle is at a distance \[r=1\]and the second, at\[r=4.\]The best estimate for the ratio of kinetic energies of the first and the second particle is closest to [JEE Main Online 16-4-2018]
A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? [JEE Main 09-Jan-2019 Morning]
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \[\,AB=BC\], and the angle made by AB with downward vertical is \[\theta \], then: [JEE Main 09-Jan-2019 Morning]
question_answer69) A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \[45{}^\circ \] at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is \[\left( g=10\text{ }m{{s}^{-}}^{2} \right)\] [JEE Main 09-Jan-2019 Evening]
question_answer70) Two forces P and Q, of magnitude 2F and 3F, respectively; are at an angle 9 with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \[\theta \] is- [JEE Main 10-Jan-2019 Evening]
A slab is subjected to two forces \[{{\vec{F}}_{1}}\]and \[{{\vec{F}}_{2}}\]of same magnitude F as shown in the figure.
Force \[{{\vec{F}}_{2}}\]is in XY-plane while force \[{{F}_{1}}\] acts along z-axis at the point \[(2\hat{i}+3j).\] The moment of these forces about point 0 will be- [JEE Main 11-Jan-2019 Morning]
question_answer72) A particle moves from the point \[(2.0\hat{i}+4.0\hat{j})m,\]at t = 0, with an initial velocity\[(5.0\hat{i}+4.0\hat{j})m{{s}^{-1}}\]. It is acted upon by a constant force which produces a constant acceleration \[(4.0\hat{i}+4.0\hat{j})m{{s}^{-2}}.\] What is the distance of the particle from the origin at time 2s? [JEE Main 11-Jan-2019 Evening]
A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is [Take \[g=10\text{ }m/{{s}^{2}}\]]
A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be (Take\[g=10m/{{s}^{2}}\]) [JEE Main 12-Jan-2019 Evening]
Two blocks A and B of masses \[{{m}_{A}}=1kg\]and \[{{m}_{B}}=3kg\]are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : (Take \[g=10\text{ }m/{{s}^{2}}\])
question_answer76) A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of \[0.70\,m{{s}^{-1}}\] with respect to the man. The speed of the man with respect to the surface is : [JEE Main Held on 12-4-2019 Morning]
question_answer77) A spring whose unstretched length is \[l\] has a force constant k. The spring is cut into two pieces of un stretched lengths \[{{l}_{1}}\]and \[{{l}_{2}}\] where, \[{{l}_{1}}=n{{l}_{2}}\]and n is an integer. The ratio \[{{k}_{1}}/{{k}_{2}}\]of the corresponding force constants, \[{{k}_{1}}\]and \[{{k}_{2}}\]will be : [JEE Main 12-4-2019 Afternoon]
A block of mass 5 kg is (i) pushed in case and (ii) pulled in case , by a force F = 20 N, making an angle of \[30{}^\text{o}\] with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is \[\mu =0.2.\]The difference between the accelerations of the block, in case and case will be : \[(g=10m{{s}^{-2}})\]
question_answer79) A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of \[45{}^\circ \] with the vertical. Then F equals: (Take \[g=10\text{ }m{{s}^{2}}\] and the rope to be massless) [JEE MAIN Held on 07-01-2020 Evening]
question_answer80) A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed \[\omega \] about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is [JEE MAIN Held On 08-01-2020 Morning]
question_answer81) A body A, of mass \[m\text{ }=\text{ }0.1\text{ }kg\] has an initial velocity of \[3\hat{i}\,m{{s}^{1}}\]. It collides elastically with another body, B of the same mass which has an initial velocity of\[5\hat{j}\text{ }m{{s}^{1}}\]. After collision, A moves with a velocity \[\vec{v}=4\left( \hat{i}+\hat{j} \right)\] . The energy of B after collision is written as \[\frac{x}{10}J.\] the value of x is ________. [JEE MAIN Held On 08-01-2020 Morning]
A spring mass system (mass m, spring constant k and natural length l) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc.
If the disc together with spring mass system, rotates about its axis with an angular velocity \[\omega ,\] \[(k>>m\,{{\omega }^{2}})\] the relative change in the length of the spring is best given by the option