Consider the situation as shown in the figure. All the surface are smooth and the string and pulley are light. Find the mass of the hanging block which will prevent the smaller block form slipping over the triangular block.

Options

A. `(M + m)/(cot theta - 1)`
B. `(M - m)/(cot theta - 1)`
C. `(M + m)/(cot theta + 1)`
D. `(m - n)/(M + m) tan theta`

Answer

A

Explanation

`T - N sin theta = Ma`
`N sin theta = ma` and `N cos theta = mg`, mg - T = Ma

Solving for M', we get :
`M' = (M + m)/(cot theta - 1)`
Alternate method
`a = ("net pulling force")/("Total mass") = (M'g)/(M + m + M')`
Since m is not sliding on M , in the absence of friction `a = g tan theta` (as discussed in the class)
by solving
`g tan theta = (M'g)/(M + m + M') implies M' = (M + m)/(cot theta - 1)`