- Home
- Standard 11
- Physics
13.Oscillations
medium
A clock $S$ is based on oscillations of a spring and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having same density as earth but twice the radius then
A
$S$ will run faster than $P$
B
$P$ will fun faster than $S$
C
Both run at same rate
D
Both runat same rate but different than earth
Solution
(b)
Time period of spring $=2 \pi \sqrt{\frac{k}{m}}$
Time period of pendulum $=2 \pi \sqrt{\frac{l}{g}}$
Time period of spring will not be affected by gravitational acceleration.
Let mass of earth be $m$
Mass of new planet $=\rho \times \frac{4}{3} \pi(2 R)^3=8 m$
$g_2=\frac{G M_2}{\left(R_2\right)^2}=\frac{G \times 8 M}{(2 R)^2}=2 g$
$T_2=2 \pi \sqrt{\frac{I}{2 g}}$
$T_2=\frac{T}{\sqrt{2}}$
Hence $P$ will move faster.
Standard 11
Physics
