Q. A mass M, attached to a spring, Oscillates with a period of 2 s. If the mass is increased by 4 kg, the time period increases by 1 s. Assuming that Hooke’s law is obeyed, the initial mass M was
A) 3.2 kg
B) 1 kg
C) 2 kg
D) 8 kg
Explanation
(a) $T = 2 = 2\pi\sqrt{\frac{M}{k}}$
and $2 + 1 = 2\pi\sqrt{\frac{M + 4}{k}}$
or $3 = 2\pi\sqrt{\frac{k + 4}{k}}\ \ \ so\ \ \frac{4}{9} = \frac{M}{M + 4}$
or $4M + 16 = 9\ M\ \ or\ \ \ M = \frac{16}{5} = 3.2\ kg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.