1
WB JEE 2021
+1
-0.25
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?
A
(3, 1, 8)
B
(0, 0, 0)
C
(1, 3, 2)
D
($$-$$1, 2, 3)
2
WB JEE 2018
+2
-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?
A
$${{{\rho _2}} \over {{\rho _1}}}$$$${{{\left( {1 - {{{\rho _2}} \over {{\rho _1}}}} \right)}^{{5 \over 3}}}}$$
B
$${{{\rho _2}} \over {{\rho _1}}}\left[ {1 - {{\left( {1 - {{{\rho _2}} \over {{\rho _1}}}} \right)}^{{5 \over 3}}}} \right]$$
C
$${{{\rho _2}} \over {{\rho _1}}}$$$${{{\left( {1 - {{{\rho _1}} \over {{\rho _2}}}} \right)}^{{5 \over 3}}}}$$
D
$${{{\rho _2}} \over {{\rho _1}}}\left[ {1 - {{\left( {1 - {{{\rho _1}} \over {{\rho _2}}}} \right)}^{{5 \over 3}}}} \right]$$
3
WB JEE 2017
+1
-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
A
zero
B
v
C
$${{3v} \over 2}$$
D
$$-$$ $${{3v} \over 2}$$
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Medical
NEET