Question

A trolley of mass 20 kg is attached to a block of mass 4 kg by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between trolley and the surface is 0.02, then the acceleration of the trolley and block system is:
(Take g = 10 $m{s}^{-2}$)

• A. 1$m{s}^{-2}$
• B. 2 $m{s}^{-2}$
• C. 1.5 $m{s}^{-2}$
• D. 2.5 $m{s}^{-2}$

Answer 1

The correct option is C 1.5 $m{s}^{-2}$

As the string is inextensible, and the pulley is smooth, therefore both the 4 kg block and the 20 kg trolley have the same acceleration a.
Let T be tension in the string.
The equation of motion of the block is
$40-T=4a$ ..........(i)
The equation of motion of the trolley is
T - $f_k$=20a$
$f_k=\mu N$
Here, ${\mu }_k=0.02,N=20\times 10=200N$
$\therefore T-0.02\times 200=20a$ or$T-4=20a$ .................(ii)
Adding (i) and (ii), we get, $a=\frac{36}{24}m{s}^{-2}=1.5m{s}^{-2}$