Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NTA Abhyas 2020 · Physics · Center of Mass, Momentum and Collision

A spherical cavity is made in a lead sphere of radius R such that...

A spherical cavity is made in a lead sphere of radius RR such that its surface touches the outside surface of lead sphere and passes through the centre. The shift in the centre of mass of the lead sphere as a result of this hollowing, is

A spherical cavity is made in a lead sphere of radius R such that its surface touches the outside surface of lead

Options

  1. AR7\dfrac{\text{R}}{7}
  2. BR14\dfrac{\text{R}}{14}
  3. CR2\dfrac{\text{R}}{2}
  4. DR

Correct answer

B. R14\dfrac{\text{R}}{14}

Step-by-step solution

Let centre of mass of lead sphere after hollowing be at point O2{O}_{2}, where OO2=x{OO}_{2} = x

Mass of spherical hollow m=43π(R2)2M(42\piR3)=M8m = \dfrac{4}{3}\pi\left(\dfrac{R}{2}\right)^{2}\text{M}\left(\dfrac{4}{2}\piR^{3}\right) = \dfrac{M}{8} and

x=OO1=R2\text{x} = {OO}_{1} = \dfrac{R}{2}

A spherical cavity is made in a lead sphere of radius R such that its surface touches the outside surface of lead

∴x=M×0−(M8)×R2M−M8=MR167M8=−R14∴ \text{x} = \dfrac{\text{M} \times 0 - \left(\dfrac{M}{8}\right) \times \dfrac{R}{2}}{\text{M} - \dfrac{M}{8}} = \dfrac{\text{MR}16}{7\text{M}8} = - \dfrac{R}{14}

∴shift=R14∴ \text{shift} = \dfrac{\text{R}}{1 4}
Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

Two identical bodies A and B of equal masses have initial velocities v_1 = 4 i m/s and… JEE Main 2026The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect… JEE Main 2026Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which… JEE Main 2026The position of an object having mass 0.1 kg as a function of time t is given as r =… JEE Main 2026A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses… JEE Main 2026In a perfectly inelastic collision, two spheres made of the same material with masses 15… JEE Main 2026Given below are two statements : Statement I : For a mechanical system of many particles… JEE Main 2026In a scattering experiment, a particle of mass 2 m collides with another particle of mass… JEE Advanced 2025 Full Center of Mass, Momentum and Collision list All NTA Abhyas JEE Main PYQs