If kinetic energy of a body becomes four times, then its new momentum will:

Question

If kinetic energy of a body becomes four times, then its new momentum will: (A) become four times its initial value (B) become two times its initial value (C) become half of its initial value (D) remain constant

Tardigrade Admin · Accepted Answer

The relation between kinetic energy K, and momentum p is p=√2 mK where m is mass of the body. Given, K1=K, K2=4 K , ∴ (p1/p2)=(√2 mK/√2 m (4K))=(1/2) ⇒ p2=2 p1 Hence, momentum becomes two times of its initial value.

Q. If kinetic energy of a body becomes four times, then its new momentum will:

become four times its initial value

become two times its initial value

become half of its initial value

remain constant

The relation between kinetic energy $K$ ,
and momentum $p$ is $p = 2 m K$
where m is mass of the body.
Given, $K_{1} = K, K_{2} = 4 K$ ,
$∴ \frac{p _{1}}{p _{2}} = \frac{2 m K}{2 m ( 4 K )} = \frac{1}{2}$
$\Rightarrow p_{2} = 2 p_{1}$
Hence, momentum becomes two times of its initial value.

Q. If kinetic energy of a body becomes four times, then its new momentum will:

become four times its initial value

become two times its initial value

become half of its initial value

remain constant

The relation between kinetic energy K, and momentum p is p=2mK​ where m is mass of the body. Given, K1​=K,K2​=4K , ∴p2​p1​​=2m(4K)​2mK​​=21​ ⇒p2​=2p1​ Hence, momentum becomes two times of its initial value.

The relation between kinetic energy $K$ ,
and momentum $p$ is $p = 2 m K$
where m is mass of the body.
Given, $K_{1} = K, K_{2} = 4 K$ ,
$∴ \frac{p _{1}}{p _{2}} = \frac{2 m K}{2 m ( 4 K )} = \frac{1}{2}$
$\Rightarrow p_{2} = 2 p_{1}$
Hence, momentum becomes two times of its initial value.