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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
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 $P$
  • ✓
    $P$ will fun faster than $S$
  • C
    Both run at same rate
  • D
    Both runat same rate but different than earth
✓

Answer

Correct option: B.
$P$ will fun faster than $S$
b
(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.

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