Question

The momentum of a body is numerically equal to its kinetic energy. The velocity of the body is

• A. 1 ms${}^{-1}$
• B. 4 ms${}^{-1}$
• C. 8 ms${}^{-1}$
• D. 2 $m{s}^{-1}$

Answer 1

Answer: (D)

2 $m{s}^{-1}$

Let, m be the mass of the body and v be the velocity of the body.
Now, momentum of the body is
$p=mv$
Kinetic energy is
$E=\frac{1}{2}m{v}^2$
As per given condition
$\frac{1}{2}m{v}^2=mv=x\left(say\right)$
$\frac{1}{2}m{v}^2=x$
$\frac{1}{2m}{m}^2{v}^2=x$
$\frac{1}{2m}{x}^2=x$
$x=2m$
Now,
$mv=2m$
$v=2m{s}^{-1}$