Question

Consider the situation shown in the figure. Both the pulleys and the string are light and all the surfaces are smooth.
(a) Find the acceleration of 1kg block.
(b) Find the tension in the string.

Answer 1

Given,

Two blocks of mass $1kg,2kg$

So,

$ma-2T=0$

$ma=2T$

$T=\frac{ma}{2}$

Since

$T+ma-mg=0$

$\frac{ma}{2}+ma-mg=0$

$3ma=2mg$

$a=\frac{2}{3}g$

Thus the accelerationn of $1kg$ box is $\frac{2}{3}g$

Now,

B) The tension in the string is:

$\frac{ma}{2}=\frac{2\times 2}{3}g$

$=\frac{4}{3}g$