question_answer

If the mass of a body is changed to 16 times, then what should be the change in velocity, such that its K.E remains same?

Answer:

\[{{m}_{2}}=16\,{{m}_{1}}\] \[{{V}_{2}}=?\] \[K{{E}_{1}}=K{{E}_{2}}\] \[\frac{1}{2}{{m}_{1}}v_{1}^{2}=\frac{1}{2}{{m}_{2}}v_{2}^{2}\] \[\Rightarrow {{m}_{1}}v_{1}^{2}=16{{m}_{1}}\times v_{2}^{2}\] \[\Rightarrow {{V}_{2}}=\sqrt{\frac{V_{1}^{2}}{16}}=\frac{{{V}_{1}}}{4}\] Velocity should decrease to one-four times the initial