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 $g = 10ms^{- 2}$) :

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

Answer 1

Answer: (C)

$1.5ms^{- 2}$

Answer 2

As the string is inextensible, and the pulley is smooth, therefore both the 4kg 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

$T - f_{k} = 20a$

$f_{k} = \mu_{k}N$

Here $\mu_{k} = 0.02N = 20 \times 10 = 200N$

$\therefore T - 0.02 \times 200 = 20a$

Or $T - 4 = 20a$…. (ii)

Adding (i) and (ii) we get

$a = \frac{36}{24}ms^{- 2} = 1.5ms^{- 2}$