List of top Physics Questions on Relative Motion

Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity \( v_1 \) in time \( t_1 \). On another day, if she remains stationary on the escalator moving with velocity \( v_2 \), the escalator takes her up in time \( t_2 \). The time taken by her to walk up with velocity \( v_1 \) on the moving escalator will be:
Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h.Velocity of train B with respect to A and velocity of ground with respect to B are (in m/s) :
The ratio of the radii of a planet and the earth is \( 1:2 \), the ratio of their mean densities is \( 4:1 \). If the acceleration due to gravity on the surface of the earth is \( 9.8 \, ms^{-2} \), then the acceleration due to gravity on the surface of the planet is?
A circular plate of radius \( r \) is removed from a uniform circular plate P of radius \( 4r \) to form a hole. If the distance between the centre of the hole formed and the centre of the plate P is \( 2r \), then the distance of the centre of mass of the remaining portion from the centre of the plate P is?
In a Doppler effect experiment, initially an observer and the source are moving towards each other with equal speeds. The observed frequency in this case is found to be \( f_0 \). The observed frequency once they cross each other is found to be \( f' \). If \( f \) is the frequency at the source, \( f' \) is equal to:
A hollow cylinder and a solid cylinder initially at rest at the top of an inclined plane are rolling down without slipping. If the time taken by the hollow cylinder to reach the bottom of the inclined plane is \( 2 \) s, the time taken by the solid cylinder to reach the bottom of the inclined plane is?
A block kept on a frictionless horizontal surface is connected to one end of a horizontal spring of constant \( 100 \, \text{Nm}^{-1} \), whose other end is fixed to a rigid vertical wall. Initially, the block is at its equilibrium position. The block is pulled to a distance of \( 8 \) cm and released. The kinetic energy of the block when it is at a distance of \( 3 \) cm from the mean position is?
A ball P of mass \( 0.5 \) kg moving with a velocity of \( 10 \, ms^{-1} \) collides with another ball Q of mass \( 1 \) kg at rest. If the coefficient of restitution is \( 0.4 \), the ratio of the velocities of the balls P and Q after the collision is?
A person walks up a stalled escalator in 90s. When standing on the same moving escalator, he reached in 60s. The time it would take him to walk up the moving escalator will be:
A truck moving with a constant velocity \( 12 \, \text{ms}^{-1} \) crosses a car moving from rest with uniform acceleration \( 2 \, \text{ms}^{-2} \). The distance the car has to travel from the starting point to cross the truck again is:
A swimmer wants to cross a river which is flowing at a speed 'v'. If the swimmer can swim in still water at speed 'V', the direction he should swim to cross the river in least time is
A girl of mass 30 kg stands at one end of a plank of mass 120 kg and length 4 m. Initially the plank lies at rest on a horizontal frictionless surface. If the girl walks to the other end of the plank, the distance that the girl moves relative to the ground is:
The time taken by a boat to travel upstream to a certain distance and return back is 14 hours. If the velocity of boat in still water is 35 kmh$ ^{-1} $ and velocity of the stream is 5 kmh$ ^{-1} $, the distance travelled by the boat before it returns is
A drone is flying due west, a little above the train, with a speed of 10 m/s. A 270 meter long train is moving due east at a speed of 20 m/s. The time taken by the drone to cross the train is:
A student is at a distance of 16 m from a bus. The bus starts accelerating from rest with $ a = 9 \, \text{m/s}^2 $. The minimum velocity with which the student should run towards the bus to catch it is $ \alpha \sqrt{2} \, \text{m/s} $. Find $ \alpha $.
A ball is projected from the ground into the air. At a height of 5 m, its velocity is \( \vec{v} = (5 \hat{i} + 5 \hat{j}) \, \text{m/s} \). The maximum height reached by the ball is: \( (g = 10 \, \text{m/s}^2) \)
Two forces of magnitude 4 N act on an object of mass 1 kg: \( \vec{F}_1 \) at 30° to x-axis and \( \vec{F}_2 \) along y-axis. Find the magnitude of acceleration.
A car travels with a speed of 40 km/h. Rain drops fall vertically but the traces on the side window make an angle of \( 30^\circ \) with the vertical. Find the magnitude of rain’s velocity with respect to the car.
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be