1
WB JEE 2022
+1
-0.25

Three particles, each of mass 'm' grams situated at the vertices of an equilateral $$\Delta$$ABC of side 'a' cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC in g-cm2 units will be

A
2 ma2
B
$${3 \over 2}$$ ma2
C
$${3 \over 4}$$ ma2
D
$${5 \over 4}$$ ma2
2
WB JEE 2021
+1
-0.25
A uniform thin rod of length L, mass m is lying on a smooth horizontal table. A horizontal impulse P is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is
A
$${{{P^2}} \over m}$$
B
$${{7{P^2}} \over {8m}}$$
C
$${{13{P^2}} \over {2m}}$$
D
$${{2{P^2}} \over m}$$
3
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)
4
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
$${{{\rho _2}} \over {{\rho _1}}}\left[ {1 - {{\left( {1 - {{{\rho _1}} \over {{\rho _2}}}} \right)}^{{5 \over 3}}}} \right]$$
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