Question

Find the mass M of the hanging block in figure (5−E16) that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.

Answer 1

Given :

Block ‘m’ will have the same acceleration as that of M’, as it does not slip over M‘.

Refer the attachment for the Free body diagrams,

T + Ma – Mg = 0    …(i)

T – M’a – Rsinθ = 0    …(ii)

Rsinθ – ma = 0

Rcosθ – mg = 0

Eliminating T, R and a from the above equations, we get:

M=M’+m/cot θ-1

Answer 2

This is the required mass of the hanging block