A mass of 100 g strikes the wall with speed `5 m//s` at an angle as shown in figure and it rebounds with the same speed it the contact time is `2 xx 10^(-3) sec`. What is the force applied on the mass by the wall :

Options

A. `250sqrt3` N to right
B. 250 N to right
C. `250sqrt3` N to left
D. 250 N to left

Answer

C

Explanation

Force= Rate of change of momentum
Initial momentum `vec(P)_(1)= mv sin theta hat(i) + mv cos theta hat(j)`
Final momentum `vec(P)_(2)= -mv sin theta hat(i) + mv cos theta hat(j)`
`therefore vec(F)= (Delta vec(P))/(Delta t)= (-2mv sin theta)/(2 xx 10^(-3))`
Substituting `m= 0.1kg, v= 5 m//s, theta= 60^(@)`
Force on the ball `vec(F)= -250 sqrt3N`
Negative sign indicates direction of the force.