Question

A block of metal weighing $2kg$ is resting on a frictionless plane. It is struck by a jet releasing water at a rate of$1kg/s$ and at a speed of $5m/s$.The initial acceleration of the block will be

• A. $2.5m/s^2$
• B. $0.5m/s^2$
• C. $10m/s^2$
• D. $20m/s^2$

Answer 1

The correct option is A $2.5m/s^2$

Given that,

Mass $m=2kg$

The speed of water $v=5m/s$

The final velocity of mass of water after hitting the metal block is zero.

So, the average change in momentum per sec = initial momentum

$=m\times v$

$\frac{dp}{dt}=1\times 5$

$\frac{dp}{dt}=5kgm/s$

A this change in momentum occurs during $1sec$.

We may say that the force exerted on the $2kg$ metal block is

$F=\frac{changeinmomentum}{time}$

$F=\frac{5}{1}=5N$

So, By Newton's law initial acceleration of the block is

$F=ma$

$a=\frac{F}{m}$

$a=\frac{5}{2}m/s^2$

Hence, D is correct ,