EASY
JEE Main/Advance
IMPORTANT
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A rigid body consists of a 3 kg mass connected to a 2 kg mass by a massless rod. The 3 kg mass is located at r1=(2i^+5j^)m and the 2 kg mass at r2=(4i^+2j^)m. If coordinates of the centre of mass is (a, b) then 511(a+b) will be :

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Important Questions on Centre of Mass, Momentum and Collisions

EASY
JEE Main/Advance
IMPORTANT

Three rods of the same mass are placed as shown in the figure. If sum of the coordinates of the centre of mass of the system is ka3 then k is :

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MEDIUM
JEE Main/Advance
IMPORTANT

A man has constructed a toy as shown in figure. If density of the material of the sphere is 12 times of the cone, if position of the centre of mass is at αR from O, then α=.......
[Centre of mass of a cone of height h is at a height of h4 from its base]

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EASY
JEE Main/Advance
IMPORTANT

If the centre of gravity of a thin homogeneous plate having the form of a rectangle with sides r and 2r from which a semicircle with a radius ris cut out of figure is 2rα(4-π) from O, then α= ?

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EASY
JEE Main/Advance
IMPORTANT

A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge of the plate as shown in figure. Find the position of the centre of mass of the remaining portion from centre of bigger circle.

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MEDIUM
JEE Main/Advance
IMPORTANT

A thin sheet of metal of uniform thickness is cut into the shape bounded by the line x=a and y=±kx2, as shown. If sum of the coordinates of the centre of mass is αa4 then α will be?

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HARD
JEE Main/Advance
IMPORTANT

A ball of mass 100 g is projected vertically upwards from the ground with a velocity of 49 m s-1. At the same time another identical ball is dropped from a height of 98 m to fall freely along the same path as that followed by the first ball. After some time the two balls collide and stick together and finally fall to the ground. The time of flight of the masses is 5+x2 s. Write the value of x.

(Take g=9.8 m s-2)

MEDIUM
JEE Main/Advance
IMPORTANT
A sphere of mass m1 in motion hits directly another sphere of mass m2 at rest and sticks to it, the total kinetic energy after collision is 23 of their total K.E. before collision. The ratio of m1:m2 is x:1. Find the value of x.
HARD
JEE Main/Advance
IMPORTANT

A simple pendulum is suspended from a peg on a vertical wall. The pendulum is pulled away from the wall to, a horizontal position (see fig.) and released. The ball hits the wall, the coefficient of restitution being 25. What is the minimum number of collisions after which the amplitude of oscillations becomes less than 60 degrees?

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