Question

A $4$ $kg$ block is on a smooth horizontal table. The block is connected to a second block of mass $1$ $kg$ by a massless flexible taut cord that passes over a frictionless pulley. The $1$ $kg$ block is $1$ $m$ above the floor. The two blocks are released from rest. With what speed does the $1$ $kg$ block hit the ground?

• A. $3m{s}^{-1}$
• B. $2.5m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $1.5m{s}^{-1}$

Answer 1

The correct option is C $2m{s}^{-1}$

Let the tension in the cord be $T$ and the acceleration of the blocks be $a$.

Thus $T=m_{2}a$

and $m_{1}g-T=m_{1}a$

$⟹a=\frac{m_{1}g}{m_1+m_2}$

$=\frac{1}{1+4}g=\frac{g}{5}=2m/s^2$

Thus the velocity of block of mass $m_1=1kg$ when it reaches the bottom=$\sqrt{2as}=\sqrt{2\times 2\times 1}m/s=2m/s$