A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )
At correct rate
$6$ time faster
$\sqrt 6 $ times faster
$\sqrt 6 $ times slowly
Answer the following questions:
$(a)$ Time period of a particle in $SHM$ depends on the force constant $k$ and mass $m$ of the particle:
$T=2 \pi \sqrt{\frac{m}{k}}$. A stmple pendulum executes $SHM$ approximately. Why then is the time pertodof.anondwers period of a pendulum independent of the mass of the pendulum?
$(b)$ The motion of a simple pendulum is approximately stmple harmonte for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that $T$ is greater than $2 \pi \sqrt{\frac{l}{g}} .$ Think of a qualitative argument to appreciate this result.
$(c)$ A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?
$(d)$ What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely failing under gravity?
A second's pendulum is placed in a space laboratory orbiting around the earth at a height $3R$, where $R$ is the radius of the earth. The time period of the pendulum is
The periodic time of a simple pendulum of length $1\, m $ and amplitude $2 \,cm $ is $5\, seconds$. If the amplitude is made $4\, cm$, its periodic time in seconds will be
A pendulum of length $2\,m$ lift at $P$. When it reaches $Q$, it losses $10\%$ of its total energy due to air resistance. The velocity at $Q$ is .... $m/sec$
The length of a seconds pendulum is .... $cm$