A uniform cubical block of mass M is attached to a pulley. One end of a string, passing over the pulley is fixed to a light pole while is fixed on the bigger block and its another end is attached to a block of mass m as shown in figure. The maximum value of the mass m so that the block does not topple is : (string and pulley are ideal)

Options

A. `(Ml_(1))/((l_(2)-l_(1)))`
B. `(2Ml_(1))/((l_(2)-l_(1)))`
C. `(Ml_(1))/(2(l_(2)-l_(1)))`
D. `(M(l_(1)+l_(2)))/(2l_(1))`

Answer

C

Explanation

When the block is about to tople contact force will pass through A and net torque about A will be zero `mg(l_(2)-k_(1))=Mg l_(1)//2`
`mg(l_(2)-l_(1))Mg l_(1)//2`
or `m=(Ml_(1))/(2(l_(2)-l_(1)))`