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 accderal ion of the trolley and block system is `("Take" g=10ms^(-2))`

Options

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

Answer

C

Explanation

As the string in inextensible, and pulley is smooth, therefore both 4kg block and the 20 kg trolly have the same acceleration a.
Let T be tension in the string. The equation of motion of the block is 40-T=4a
The equation of motion of the trolley is `T-f_(k)=20a`
`f_(k)=mu_(k)N`
`Here, mu_(k)=0.02, N=20xx10=200N `
`therefore T-0.02xx200=20a or T-4=20a....(ii)`
Adding (i) and (ii), we get `a=(36)/(24)ms^(-2)=1.5ms^(-2)`