If the kinetic energy of a body becomes 256 times its initial value, then the new linear momentum will be:

The correct answer is C, 16 times the initial value. Kinetic energy depends on the square of the momentum, so the momentum grows as the square root of the energy. For a body of mass m, the kinetic energy can be written as p squared divided by 2m, where p is the linear momentum. If the mass does not change, p equals the square root of 2mE, so p is proportional to the square root of E. When the kinetic energy becomes 256 times, the momentum becomes the square root of 256, that is 16 times its earlier value, and the speed also becomes 16 times. Option A is wrong because a body cannot gain energy while its momentum stays the same. Option B is wrong because 8 times the momentum would make the energy 64 times, not 256 times. Option D is wrong because 32 times the momentum would make the energy 1024 times. Exam tip: E equals p squared by 2m, so if the energy becomes n times the momentum becomes root n times, and if the momentum becomes n times the energy becomes n squared times.