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Class XI Physics System of Particles & Rotational Motion 7

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Question 1

A uniform thin rod AB of length L has linear mass density

, where x is measured from A. If the CM of the rod lies at a distance of

from A, then a and b are related as:

Question 2

Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is

Question 3

A solid cylinder of mass M and radius R rolls without slipping down on inclined plane of length L and height h. What is the speed of its centre of mass, when the cylinder reaches its bottom?

Question 4

A diatomic molecule is formed by two atoms which may be treated as mass points m₁ and m₂ joined by a massless rod of length r. The, the moments of inertia of the molecule about an axis passing through the centre of mass and perpendicular to rod in

Question 5

There identical spheres of mass m each are placed at the corners of an equilateral triangle of side 2 m. Taking one of the corner as the origin, the position vector of the centre of mass is

Question 6

A rigid body in the shape of a “V” has two equal arms made of uniform rods. What must the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?

Question 7

A 500 kg boat is 9 m long and is floating without motion on still water. A man of mass 100 kg is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

Question 8

A circular turntable of radius 0.5 m has a smooth groove as shown in the figure. A ball of mass 90 g is placed inside the groove along with a spring of spring constant 10² N/cm. The ball is at a distance of 0.1 m from the center when the turntable is at rest. On rotating the turntable with a constant angular frequency of 10² sec^-1, the ball moves away from the center by a distance nearly equal to

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Sep 30JEE & BITSAT