Question

If the mass of a block is increased four time
find the factor by which its speed should
change so that its kinetic energy remains the same​

Answer 1

GIVEN :

• Initial energy = KE
• Initial mass = m
• Initial velocity = v

TO FIND :

• The factor by which it's speed should change so that it's kinetic energy remains the same.

FORMULA USED :

• KE = 1/2 mv²

SOLUTION :

We know that,

=> KE = 1/2 mv².

=> v^2/2 = KE/m

We will get the new values,

• New mass = m

m' = 4 m

• New KE = KE'

KE' = KE

• New velocity = v'

=> KE' = 1/2 m'v'²

=> KE = 2 mv'²

v'² = 1/2 (KE/m)

=> KE/m = v²/2

=> v'² = 1/2 × v²/2

=> v² = v²/4.

★ v' = v/2.

•°• Therefore, the speed will be halved.