JEE Main & Advanced Physics Two Dimensional Motion Question Bank

done Mock Test - Motion in Two Dimension Total Questions - 25

• question_answer1)
  A stone projected with a velocity \[u\] at an angle \[\theta \] With the horizontal reaches maximum height \[{{H}_{1}}\] When it is projected with velocity u at an angle \[(\frac{\pi }{2}-\theta )\] with the horizontal, it reaches maximum height \[{{H}_{2}}\]. The relation between the horizontal range R of the projectile, \[{{H}_{1}}\]and \[{{H}_{2}}\]is
  A)
  \[R=4\sqrt{{{H}_{1}}{{H}_{2}}}\] done clear
  B)
  \[R=\,4({{H}_{1}}-{{H}_{2}})\] done clear
  C)
  \[R=\,4({{H}_{1}}+{{H}_{2}})\] done clear
  D)
  \[R=\,\frac{{{H}^{2}}_{1}}{{{H}^{2}}_{2}}\] done clear
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• question_answer2)
  A man standing on the roof of a house of height \[h\] throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth's surface will be
  A)
  \[\sqrt{2gh+{{u}_{^{^{{}}}}}^{2}}\,:u\] done clear
  B)
  \[1:2\] done clear
  C)
  \[1:1\]               done clear
  D)
  \[\sqrt{2gh+{{u}^{2}}\,}:\sqrt{2gh}\] done clear
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• question_answer3)
  A particle is projected from point \[O\] with velocity \[u\] in a direction making an angle \[\alpha \] with the horizontal. At any instant its position is at point \[p\] at right angles to the initial direction of projection, Its velocity at point \[p\] is
  A)
  \[u\tan \alpha \]             done clear
  B)
  \[u\cot \alpha \] done clear
  C)
  \[u\operatorname{cosec}\alpha \] done clear
  D)
  \[u\sec \alpha \] done clear
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• question_answer4)
  Pankaj and Sudhir are playing with two different balls of masses m and \[2m\], respectively. If Pankaj throws his ball vertically up and Sudhir at an angle\[\theta \], both of them stay in our view for the same period. The height attained by the two balls are in the ratio
  A)
  2 : 1                 done clear
  B)
  1 : 1 done clear
  C)
  \[1:cos\theta \]   done clear
  D)
  \[1:sec\theta \] done clear
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• question_answer5)
  A ship A sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h, to a person, sitting in a moving ship \[B\]. Determine the velocity (absolute) of ship \[B\].
  A)
   \[5\sqrt{5}\,km/h,\,ta{{n}^{-1}}(1/2)\,S\,of\,E\] done clear
  B)
   \[5\sqrt{5}\,km/h,\,ta{{n}^{-1}}(1/2)\,E\,of\,S\] done clear
  C)
  \[4\sqrt{5}\,km/h,\,ta{{n}^{-1}}(1/2)\,S\,of\,E\] done clear
  D)
  \[4\sqrt{5}\,km/h,\,ta{{n}^{-1}}(1/2)\,E\,of\,S\] done clear
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• question_answer6)
  A particle is projected with a certain velocity at an angle \[\alpha \] above the horizontal from the foot of an inclined plane of inclination\[30{}^\circ \]. If the particle strikes the plane normally, then \[\alpha \] is equal to
  A)
  \[30{}^\circ +\,te{{n}^{-1}}(\frac{\sqrt{3}}{2})\] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[60{}^\circ \]              done clear
  D)
  \[30{}^\circ \,+\,te{{n}^{-1}}(2\sqrt{3})\] done clear
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• question_answer7)
  Two balls A and B are thrown with speeds \[u\] and u/2, respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is \[15{}^\circ \] with the horizontal, then the angle of projection of A is
  A)
  \[{{\sin }^{-1}}\left( \frac{1}{8} \right)\] done clear
  B)
  \[\frac{1}{2}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] done clear
  C)
  \[\frac{1}{3}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] done clear
  D)
  \[\frac{1}{4}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] done clear
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• question_answer8)
  A particle is projected with a certain velocity at an angle \[\alpha \] above the horizontal from the foot of an inclined plane of inclination\[30{}^\circ \]. If the particle strikes the plane normally, then \[\alpha \] is equal to
  A)
  \[{{30}^{{}^\circ }}+{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] done clear
  B)
  \[{{45}^{0}}\] done clear
  C)
  \[{{60}^{0}}\]                        done clear
  D)
  \[{{30}^{0}}+{{\tan }^{-1}}(2\sqrt{3})\] done clear
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• question_answer9)
  A boy projects a stone vertically perpendicular to the trolley car with a speed \[v\]. If the trolley car moves with \[u\]constant velocity m, the time of flight of the stone is:
  A)
  \[\frac{u+v}{g}\]          done clear
  B)
  \[\frac{2v}{g}\] done clear
  C)
  \[\frac{2u}{g}\]             done clear
  D)
  none of these done clear
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• question_answer10)
  A bird is flying towards north with a velocity \[40km\,{{h}^{-1}}\]and a train is moving with velocity \[40km\,{{h}^{-1}}\] towards east. What is the velocity of the bird noted by a man in the train?
  A)
   \[40\sqrt{2}\,km\,{{h}^{-1}}\,N-E\] done clear
  B)
   \[40\sqrt{2}\,km\,{{h}^{-1}}\,S-E\] done clear
  C)
   \[40\sqrt{2}\,km\,{{h}^{-1}}\,N-W\] done clear
  D)
   \[40\sqrt{2}\,km\,{{h}^{-1}}\,S-W\] done clear
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• question_answer11)
  A person walks at the rate of \[3\,km/hr\]. Rain appears to him in vertical direction at the rate of \[3\sqrt{3}km/hr\]. Find the magnitude and direction of true velocity of rain.
  A)
   \[6\,km/hr\], inclined at an angle of \[45{}^\circ \] to the vertical towards the person's motion. done clear
  B)
   \[3\,km/hr\], inclined at an angle of \[30{}^\circ \] to the vertical towards the person's motion. done clear
  C)
   \[6\,km/hr\], inclined at an angle of \[30{}^\circ \] to the vertical towards the person's motion. done clear
  D)
   \[6\,km/hr\], inclined at an angle of \[60{}^\circ \] to the vertical towards the person's motion. done clear
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• question_answer12)
  A jet airplane travelling from east to west at a speed of 500\[km\,{{h}^{-1}}\]ejected out gases of combustion at a speed of 1500\[km\,{{h}^{-1}}\] with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?
  A)
   1000 \[km\,{{h}^{-1}}\] in the direction west to east done clear
  B)
   1000 \[km\,{{h}^{-1}}\] in the direction east to west done clear
  C)
   2000 \[km\,{{h}^{-1}}\] in the direction west to east done clear
  D)
   2000 \[km\,{{h}^{-1}}\] in the direction east to west done clear
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• question_answer13)
  A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively, are \[\vec{w},\,\vec{v},\,\vec{\alpha }\,and\,{{\vec{a}}_{c}}\]. Which of the following relations is not correct?
  A)
  \[\vec{w}\bot \vec{v}\]  done clear
  B)
  \[\vec{w}\bot \vec{\alpha }\] done clear
  C)
  \[\vec{w}\bot {{\vec{\alpha }}_{c}}\]    done clear
  D)
  \[\vec{v}\bot {{\vec{\alpha }}_{c}}\] done clear
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• question_answer14)
  A stone is projected from a horizontal plane. It attains maximum height '\[H\]' and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assuming the collision to be elastic the height of the point on the wall where ball will strike is
  A)
  \[\frac{H}{2}\]              done clear
  B)
  \[\frac{H}{4}\] done clear
  C)
  \[\frac{3H}{4}\]                        done clear
  D)
  None of these done clear
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• question_answer15)
  An aircraft moving with a speed of 1000 km/h is at a height of 6000 m, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is 540 m/s, the firing angle \[\theta \] for the bullet to hit the aircraft should be
  A)
  \[73{}^\circ \]              done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[60{}^\circ \]  done clear
  D)
  \[45{}^\circ \] done clear
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• question_answer16)
  An aeroplane is to go along straight line from \[A\] to \[B\], am back again. The relative speed with respect to wind is \[V\] The wind blows perpendicular to line AB with speed v The distance between \[A\] and \[B\] is \[l\]. The total time for round trip is
  A)
  \[\frac{2\ell }{\sqrt{{{V}^{2}}-{{v}^{2}}}}\]  done clear
  B)
  \[\frac{2v\ell }{{{V}^{2}}-{{v}^{2}}}\] done clear
  C)
  \[\frac{2V\ell }{{{V}^{2}}-{{v}^{2}}}\]         done clear
  D)
  \[\frac{2\ell }{\sqrt{{{V}^{2}}+{{v}^{2}}}}\] done clear
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• question_answer17)
  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 tha they make complete circles in the same time t. The ratic of their centripetal acceleration is
  A)
  \[{{m}_{1}}\,{{r}_{1}}\,:\,{{m}_{2}}\,{{r}_{2}}\]       done clear
  B)
  \[{{m}_{1}}\,:\,{{m}_{2}}\] done clear
  C)
  \[{{r}_{1}}\,:\,{{r}_{2}}\]                    done clear
  D)
  \[1\,\,:\,\,1\]   done clear
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• question_answer18)
  Which of the following statements is false for a particle moving in a circle with a constant angular speed?
  A)
   The acceleration vector points to the centre of the circle. done clear
  B)
   The acceleration vector is tangent to the circle. done clear
  C)
   The velocity vector is tangent to the circle. done clear
  D)
   The velocity and acceleration vectors are perpendiculai to each other. done clear
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• question_answer19)
  A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from \[P\] to \[Q\] is \[(\angle POQ={{40}^{{}^\circ }})\]
  A)
  \[2v\,\cos \,40{}^\circ \] done clear
  B)
  \[2v\,\sin 40{}^\circ \] done clear
  C)
  \[2v\,\sin \,20{}^\circ \] done clear
  D)
  \[2v\,\cos \,20{}^\circ \] done clear
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• question_answer20)
  A particle is projected from the ground with an initial speed of \[v\] at an angle \[\theta \] with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is
  A)
  \[\frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta }\]    done clear
  B)
  \[\frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta }\] done clear
  C)
  \[\frac{v}{2}\sqrt{1+3{{\cos }^{2}}\theta }\] done clear
  D)
  \[v\,\cos \,\theta \] done clear
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• question_answer21)
  A flying horizontally at 8 m/s at an altitude 180m when a package of emergency medical supplies is ejected horizontally backward with a speed of 12 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance in (m) between the package and the helicopter when the package hits the ground?
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• question_answer22)
  The equation of motion of a projectile is \[Y=12x-\frac{3}{4}{{x}^{2}}\].The horizontal component of velocity is \[3\,m{{s}^{-1}}\]. What is the range in (m) of the projectile?
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• question_answer23)
  Rain is falling with speed \[12\sqrt{2}\] m/s at an angle of \[45{}^\circ \] with vertical line. A man in a glider going at a speed of \[u\]at angle of \[37{}^\circ \] with respect to ground. Find the speed in (m/s) of glider so that rain appears to him falling vertically. Consider motion of glider and rain drops in same vertical plane.
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• question_answer24)
  A plane flying horizontally at \[1000\,m{{s}^{-1}}\] releases an object which reaches the ground in 10 s. At what angle in (Degree) with horizontal it hits the ground?
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• question_answer25)
  A man who can swim at the rate of \[2\,km/hr\] (in still river) crosses a river to a point exactly opposite on the other bank by swimming in a direction of \[120{}^\circ \] to the flow of the water in the river. The velocity of the water current in km/hr is
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