Question

Two unequal masses of $1kg$ and $2kg$ are connected by an inextensible light string passing over a smooth pulley as shown in the figure. A force $F=20N$ is applied on $1kg$ block. Find the acceleration of either block. $(g=10m/s^2)$ in $m/s^2$

Answer 1

The given system can be represented as shown


Total downward force on $1kg$ mass = $F+g=20+10=30N$
And, on $2kg$ mass = $2g=20N$
Hence, $1kg$ mass will accelerate downwards
For $1kg$ mass we have,
$30-T=a$ ........... (1)
For $2kg$ mass we have,
$T-20=2a$ ...........(2)
From (1) & (2) we get
$10=3a\Rightarrow a=\frac{10}{3}m/s^2$