Question

A body is dropped from a certain height. When it loses $U$ amount of its potential energy it acquires a velocity $v$ . The mass of the body is

• A. $\frac{2 U}{v^{2}}$
• B. $\frac{2 v}{U^{2}}$
• C. $\frac{2 v}{U}$
• D. $\frac{U^{2}}{2 v}$

Answer 1

Answer: (A)

Given that
Loss in potential energy, $U_{i}-U_{f}=U$
Initial velocity, $u=0$
Final velocity $=v$ .
Let mass of the body is $=m$
Using the conservation of mechanical energy,
$U_{i}+K_{i}=U_{f}+K_{f}$
$\Rightarrow U_{i}+0=U_{f}+\frac{1}{2}mv^{2}$
$\Rightarrow U_{i}-U_{f}=\frac{1}{2}mv^{2}$
$\Rightarrow U=\frac{1}{2}mv^{2}$
$\Rightarrow m=\frac{2 U}{v^{2}}$