Question

In the figure given below, with what acceleration does the block of mass m will move? (Pulley and strings are massless and frictionless)

• A. $\frac{g}{3}$
• B. $\frac{2g}{5}$
• C. $\frac{2g}{3}$
• D. $\frac{g}{2}$

Answer 1

The correct option is C $\frac{2g}{3}$

Let the tension in the string going over pulley be $T$

And the acceleration of mass m is a $($upward direction$)$

For left side mass$,$

$T-mg=ma$

Or $,T=mg+ma$

For right side masses$,$

$5mg-T=5ma$

Or $,T=5mg-5ma$

From above equations$,$

$mg+ma=5mg-5ma$

Or $,6ma=4mg$

Or $,a=2g/3$

Hence,

option $\left(C\right)$ is correct answer.