Question

A block of mass $1\text{kg}$ is connected by a light string passing over two smooth pulleys placed on a smooth horizontal surface as shown. Another block of $1\text{kg}$ is connected to the other end of the string then acceleration of the system and tension in the string are

• A. $5{\text{ms}}^{-2},5\text{N}$
• B. $1{\text{ms}}^{-2},1\text{N}$
• C. $1{\text{ms}}^{-2},5\text{N}$
• D. $5{\text{ms}}^{-2},10\text{N}$

Answer 1

The correct option is A $5{\text{ms}}^{-2},5\text{N}$

Considering free body diagram,
$mg-T=ma$ (for hanging mass)
and $T=ma$
(for mass lying on surface)
Adding $mg=(m+m)a$
or $a=\frac{mg}{2m}$
$\therefore a=\frac{g}{2}=\frac{10}{2}=5{\text{ms}}^{-2}$
and $T=1\times 5=5\text{N}$