A block of mass m attached to a spring oscillates with a time period T on the surface of the Earth. The entire spring-mass system is then taken to a planet where the acceleration due to gravity is one-fourth that of the Earth, and the block is replaced by another block of mass 2m . The new time period of oscillation will be:

Step-by-step solution

The time period of a spring-mass system is given by T = 2 m k , where m is the mass of the block and k is the spring constant. The time period is independent of the acceleration due to gravity ( g ). Therefore, taking the system to a planet with g' = g 4 has no effect on the time period. When the mass is changed to m' = 2m , the new time period is: T' = 2 2m k = 2 ( 2 m k ) = 2 T . Answer: 2 T