Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JIPMER 2018
Exam
JIPMER
Year
2018
Subject
Physics
Chapter
Gravitation

JIPMER 2018 · Physics · Gravitation

R is the radius of Earth and ω is its angular velocity and g_p is...

R is the radius of Earth and ω\omega is its angular velocity and gpg_p is the value of gg at the poles. The effective value of gg at a latitude λ=60∘\lambda=60^{\circ}.

Options

  1. Agp−14Rω2g_p-\frac{1}{4} R \omega^2
  2. Bgp+14Rω2g_p+\frac{1}{4} R \omega^2
  3. Cgp−12Rω2g_p-\frac{1}{2} R \omega^2
  4. Dgp+12Rω2g_p+\frac{1}{2} R \omega^2

Correct answer

A. gp−14Rω2g_p-\frac{1}{4} R \omega^2

Step-by-step solution

The acceleration due to gravity at a latitude λ\lambda is g′=g−Rω2cos⁡2λ\mathrm{g}^{\prime}=\mathrm{g}-\mathrm{R} \omega^2 \cos ^2 \lambda At the poles, λ=90∘\lambda=90^{\circ} ∴g′=\therefore \quad \mathrm{g}^{\prime}=\mathrm{g}=\mathrm{g}p_{\mathrm{p}} For λ=60∘\quad \lambda=60^{\circ}, g′=gp−Rω2cos⁡2λ\mathrm{g}^{\prime}=\mathrm{g}_{\mathrm{p}}-\mathrm{R} \omega^2 \cos ^2 \lambda or g′=gp−Rω2cos⁡260∘\quad g^{\prime}=g_p-R \omega^2 \cos ^2 60^{\circ} =gp−Rω2(12)2=gp−14Rω2=g_p-R \omega^2\left(\frac{1}{2}\right)^2=g_p-\frac{1}{4} R \omega^2
Practice Gravitation on Quantrex Academy →

More from Gravitation

The amount of work done to raise a mass ' m ' from the surface of the Earth to a height… NEET 2026Two planets P_1 and P_2 with equal mass have radii R_1 and R_2 , respectively, where… NEET 2026In a solar system, the time-period of revolution of a planet tracing a circular orbit of… NEET 2026The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of… NEET 2025A body weighs 48 N on the surface of the earth. The gravitational force experienced by… NEET 2025The escape velocity for earth is v . A planet having 9 times mass that of earth and… NEET 2024The mass of a planet is (1)/(10) th that of the earth and its diameter is half that of… NEET 2024An object of mass 100 kg falls from point A to B as shown in figure. The change in its… NEET 2024 Full Gravitation list All JIPMER PYQs