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NEET PHYSICSMedium

A 100 g100 \text{ g} iron ball having velocity 10 m/s10 \text{ m/s} collides with a wall at an angle 3030^\circ and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second0.1 \text{ second}, then the force experienced by the wall is:

A

10 N10 \text{ N}

B

100 N100 \text{ N}

C

1.0 N1.0 \text{ N}

D

0.1 N0.1 \text{ N}

Step-by-Step Solution

Let the mass of the iron ball be m=100 g=0.1 kgm = 100 \text{ g} = 0.1 \text{ kg} and its velocity be v=10 m/sv = 10 \text{ m/s}. The ball collides with the wall at an angle θ=30\theta = 30^\circ with the wall. The component of velocity perpendicular to the wall before the collision is vsin30v \sin 30^\circ. Since the ball rebounds with the same angle, the component of velocity perpendicular to the wall after the collision is vsin30-v \sin 30^\circ (assuming the collision is elastic). The magnitude of the change in momentum of the ball along the normal is: Δp=m(vsin30(vsin30))=2mvsin30\Delta p = m(v \sin 30^\circ - (-v \sin 30^\circ)) = 2mv \sin 30^\circ Substituting the given values: Δp=2×0.1×10×sin30=2×1×0.5=1 kg m/s\Delta p = 2 \times 0.1 \times 10 \times \sin 30^\circ = 2 \times 1 \times 0.5 = 1 \text{ kg m/s} The force experienced by the wall is equal to the rate of change of momentum (according to Newton's second law of motion) : F=ΔpΔtF = \frac{\Delta p}{\Delta t} Given the period of contact Δt=0.1 s\Delta t = 0.1 \text{ s}: F=10.1=10 NF = \frac{1}{0.1} = 10 \text{ N} Thus, the force experienced by the wall is 10 N10 \text{ N}.

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