question_answer

A mass of 100 g strikes the wall with a speed of \[\text{5 m }{{\text{s}}^{-1}}\] at an angle as shown in figure and it rebounds with the same speed. If the contact time is \[2\times {{10}^{-3}}s,\] what is the force applied by the wall?

A) \[\text{250}\sqrt{\text{3}}\,\,\text{N to right}\]

B) \[\text{250 N to right}\]

C) \[\text{250}\sqrt{3}\text{ N to left}\]

D) \[\text{250 N to left}\]

Correct Answer: C

Solution :

Here, m = 100 g = 0.1 kg \[v=5m{{s}^{-1}},t=2\times {{10}^{-3}}s\] \[\theta =60{}^\circ \] As \[F\times t=\]Change in momentum \[=2mv\sin \theta \] Or \[F=\frac{2mv\sin \theta }{t}=\frac{2\times 0.1\times 5\times \sin 60{}^\circ }{2\times {{10}^{-3}}}\] \[=500\times \sin 60{}^\circ =250\sqrt{3}N\] to left