Question

Two masses M and m are connected at the two ends of an inextensible string. The string passes over a smooth frictionless pulley. What is the acceleration of masses and tension in the string if M is smaller then m?

• A. $(M-m)g$
• B. $mg$
• C. $\frac{2mMg}{m+M}$
• D. $\left(mM\right)mg$

Answer 1

The correct option is C $\frac{2mMg}{m+M}$

m is greater than $M$ so m will go down wards with an acceleration $a.$ Tension on both sides of the pully will be same$.$ Let it be $T.$ Let us consider forces towards mass m$.$ Here downward force is

$=mg-T$

it is also equal to $ma$

therefore$,$

$mg-T=ma$----- $\left(1\right)$

on the other side $M$ is moving upwards so upwards force$=T-Mg$ it is also equal to $Ma$ so

$T-Mg=Ma$ ------$\left(2\right)$ from $\left(1\right)$ and $\left(2\right)$

$mg-Mg=ma+Ma$

or$,a=(m-M)g/(m+M)$

also from $\left(1\right)$ and $\left(2\right)$

$T=2mMg/(m+M)$

Hence,

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