A trolley of mass 20 kg is attached to a block of mass 4kg by 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))`

Options

A. `1ms^(-2)`
B. `2ms^(-2)`
C. `1.5 ms^(-2)`
D. `2.5ms^(-2)`

Answer

C

Explanation

As the string is inextensible, and the pulley is smooth, therefore both the 4 kg Block and the 20 kg Trolley has 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_kN`
Here, `mu_k = 0.02, N= 20 xx 10 = 200`
`:. T - 0.02 xx 200 = 20a`
or T – 4 = 20a
Adding (i) and (ii), we get
`a = 36/24 ms^(-2) = 1.5 ms^(-2)`