Question

A small particle of mass `m//10` is moving horizontally at a height of `3R//2` from ground with velocity `10m//s`. A perfectly inelastic collision occurs at point `P` of surface. The mass `m` of sphere is `R`. (`m = 10 Kg` and `R = 0.1 m`) (Assume all surfaces to be smooth). Answer the following questions.

Speed of shpere just after collision is
A. `27//43 m//s`
B. `(30)/(43)m//s`
C. `(35)/(43) m//s`
D. `(40)/(43) m//s`

Answer 1

Correct Answer - B

Let `v^(1)` be the velocity of sphere after collision
`J cos 30 = 10v^(1) rArr J = (20 v^(1))/(sqrt(3))`
`J = (m)/(10)(10 cos 30)-(m)/(10)(v^(1) cos 30^(@))`
`rArr` speed of the sphere `v^(1) = (30)/(43) ms^(-1)`
speed of particle in tangential direction remains same
`10 sin 30 = 5ms^(-1)`
speed of partile `= sqrt((5)^(2)+[((30)/(43))cos 30])^(2)`
`=5.26 ms^(-1)`