Question

A trolley of mass M is attached to a block of mass m by a string passing over a frictionless pulley as shown in the figure. If the coefficient of friction between the trolley and the surface below is $\mu ,$ what is the acceleration of the trolley and the block system when they are released?

• A. $\left(\frac{m-M}{m+M}\right)g$
• B. $\frac{m}{M}g$
• C. $\left(\frac{\mu m-M}{m+M}\right)g$
• D. $\left(\frac{m-\mu M}{m+M}\right)g$

Answer 1

The correct option is D

$\left(\frac{m-\mu M}{m+M}\right)g$

If the acceleration of the block and trolley system is a, we have
$mg-T=ma........\left(1\right)$
and $T-f=Ma\Rightarrow T-\mu Mg=Ma........\left(2\right)$
Adding equations (1) and (2), $(m-\mu M)g=(m+M)a\Rightarrow a=\left(\frac{m-\mu M}{m+M}\right)g$
Hence, the correct chice is (d).