Question
A seconds pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket
A.
comes down with uniform acceleration
B.
moves round the earth in a geostationary orbit
C.
moves up with a uniform velocity
D.
moves up with uniform acceleration
Answer :
moves up with uniform acceleration
Solution :
When rocket accelerates upward with acceleration $$a,$$ then effective acceleration of rocket is $$\left( {g + a} \right).$$
As, $$T = 2\pi \sqrt {\frac{l}{g}} = 2\pi \sqrt {\left( {\frac{l}{{g + a}}} \right)} $$
Hence, period of oscillation of seconds pendulum decreases when the rocket moves up with uniform acceleration.
When rocket accelerates upward with acceleration $$a,$$ then effective acceleration of rocket is $$\left( {g + a} \right).$$
As, $$T = 2\pi \sqrt {\frac{l}{g}} = 2\pi \sqrt {\left( {\frac{l}{{g + a}}} \right)} $$
Hence, period of oscillation of seconds pendulum decreases when the rocket moves up with uniform acceleration.