WB JEE 2021 | Center of Mass Question 11 | Physics

Centre of mass (CM) of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and CM of another system of particles of 3 kg and 2 kg lies at the point ($$-$$1, 3, $$-$$2). Where should we put a particle of mass 5 kg, so that the CM of entire system lies at the CM of the first system?

(3, 1, 8)

(0, 0, 0)

(1, 3, 2)

($$-$$1, 2, 3)

WB JEE 2018

MCQ (Single Correct Answer)

-0.5

A solid spherical ball and a hollow spherical ball of two different materials of densities $$\rho $$₁ and $$\rho $$₂ respectively have same outer radii and same mass. What will be the ratio, the moment of inertia (about an axis passing through the centre) of the hollow sphere to that of the solid sphere?

$${{{\rho _2}} \over {{\rho _1}}}$$$${{{\left( {1 - {{{\rho _2}} \over {{\rho _1}}}} \right)}^{{5 \over 3}}}}$$

$${{{\rho _2}} \over {{\rho _1}}}\left[ {1 - {{\left( {1 - {{{\rho _2}} \over {{\rho _1}}}} \right)}^{{5 \over 3}}}} \right]$$

$${{{\rho _2}} \over {{\rho _1}}}$$$${{{\left( {1 - {{{\rho _1}} \over {{\rho _2}}}} \right)}^{{5 \over 3}}}}$$

$${{{\rho _2}} \over {{\rho _1}}}\left[ {1 - {{\left( {1 - {{{\rho _1}} \over {{\rho _2}}}} \right)}^{{5 \over 3}}}} \right]$$

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

Two particles A and B (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is v and the speed of B is 2v, the speed of the centre of mass is

zero

$${{3v} \over 2}$$

$$-$$ $${{3v} \over 2}$$

WB JEE 2016

MCQ (Single Correct Answer)

-0.25

Two bodies of masses m₁ and m₂ are separated by a distance R. The distance of the centre of mass of the bodies from the mass m₁ is

$${{{m_2}R} \over {{m_1} + {m_2}}}$$

$${{{m_1}R} \over {{m_1} + {m_2}}}$$

$${{{m_1}{m_2}} \over {{m_1} + {m_2}}}R$$

$${{{m_1} + {m_2}} \over {{m_1}}}R$$

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