A block of mass M slides on a frictionless surface with an initial speed of `v_(0)` On top of block is a small box of mass m. the coefficients of friction between box and block are `mu_(6) and mu_(k)`. The sliding block encounters and ideal spring with force constant K. Answer following questions. What is maximum value of k for which it remains true that box does not slide?

Options

A. `((mu_(s)g)/(v_(0)))^(2)(M)/((M+m))`
B. `((mu_(s)g)/(v_(0)))^(2)(M+m)`
C. `((mu_(s)g)/(2v_(0)))^(2)(M+m)^(2)/(M)`
D. None of these

Answer

B

Explanation

`(1)/(2)(M+m)v_(0)^(2)=(1)/(2)kx_(m)^(2)`
`kx_(m)=mu_(s)(M+m)g`
`x_(m)=(mu_(s)(M+m)g)/(k)`
`(1)/(2)(M+m)v_(0)^(2)=(1)/(2)k(((M+m)mu_(s)g)/k)^(2)`
`k=((mu_(s)g)/(v_(0)))^(2)(M+m)`