A trolley has a simple pendulum suspended from a frame fixed to itsa desk A block B is in contact on its vertical and The trolley is on horizontal rails and acceleration toward the right such that the block is just orevented from falling The value of coefficient of friction between A and B is `0.5` to the vertical is

Options

A. `tan^(-1)((1)/(2))`
B. `tan^(-1)(3)`
C. `tan^(-1)(sqrt(2))`
D. `tan^(-1)(2)`

Answer

D

Explanation

In the free body diagram of B

`N = m_(B)a` …(i)
`f = m_(B)g`
`muN = m_(B)g`…(ii)
From Eqs (i) and (ii)
`a = (g)/(mu) = 20 ms^(-2)`
FBD of bob
`T sin theta = ma`…(iii)
`T cos theta = mg`...(iv)
From Eqs (iii) and (iv)
`tan theta = (a)/(g) rArr theta = tan^(-1)(2)`