Question

The acceleration of 3 kg mass as shown in figure is:

(assume $g=10m/s^2$)

• A. $3\frac{1}{3}m/s^2$ upwards
• B. zero
• C. $16\frac{2}{3}m/s^2$ downwards
• D. $3\frac{1}{3}m/s^2$ downwards

Answer 1

The correct option is D $3\frac{1}{3}m/s^2$ downwards

Let the acceleration of lower pulley be $a$ relative to the upper pulley.

And the acceleration of $2kg$ and $3kg$ blocks relative to lower pulley be $b$ upwards and $b$ downwards respectively.

Also, if the tension in above string is $2T$, then tension in lower string will be $T$ since force on pulley has to be $0$.

Hence, balancing forces on upper pulley, $4T=80N$

or, $T=20N$

Hence for $3kg$ block,

$3\left(10\right)-20=3a$

or, $a=\frac{10}{3}=3\frac{1}{3}m/s^2$ downwards.