Calculate the acceleration (In $m/s^{2}$) of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is $0.05 .\left( g =10\; m / s ^{2},\right.$ mass of the string is negligible and no other friction exists).
NEET 2020, Medium
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F. B. D. of trolly
$T - f = m _{ T } a$
$f=\mu m_{T} g$
$f=0.05 \times 10 \times 10$
$f=5 N$
$T -5=10 a$
F.B.D. of block
$m_{b} g-T=m_{b} a$
$2 \times 10-T=2 a$
$20- T =2 a$
Equation (i) $+$ (ii)
$15=12 a$
$a =\frac{15}{12} \Rightarrow a =1.25 m / s ^{2}$
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