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STD 11 - 7. gravitation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 7. gravitation4 Marks
MCQ
A clock $S$ is based on oscillation 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 the same density as earth but twice the radius
  • A
    $S$ will run faster than $P$
  • ✓
    $P$ will run faster than $S$
  • C
    They will both run at the same rate as on the earth
  • D
    None of these
✓

Answer

Correct option: B.
$P$ will run faster than $S$
b
(b) $g = \frac{4}{3}\pi \rho GR$. If density is same then $g \propto R$

According to problem ${R_p} = 2{R_e}$ $\therefore$ ${g_p} = 2{g_e}$

For clock $P$ (based on pendulum motion) $T = 2\pi \sqrt {\frac{l}{g}} $

Time period decreases on planet so it will run faster because ${g_p} > {g_e}$

For clock $S$ (based on oscillation of spring)$T = 2\pi \sqrt {\frac{m}{k}} $

So it does not change.

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