What change should be affected in the velocity of the body to maintain same kinetic energy if its mass is increased four times ?

Explanation

Since `E_k = (1)/(2)m upsilon^2,` the velocity should be reduced to half its previous value to have to have the saem kinetic energy when mass is increased to four times. This is clear from the following discussion.
`(1)/(2)m_1 upsilon_1^2 = (1)/(2)m_2 upsilon_2^2 or (upsilon_2^2)/(upsilon_1^2) = (m_1)/(m_2) or (upsilon_2)/(upsilon_1) = sqrt((m_1)/(m_2)) = sqrt((1)/(4)) = (1)/(2), i.e., upsilon^2 =(1)/(2)upsilon_1.`