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Mechanics
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With what minimum speed v must a small ball should be pushed inside a smooth vertical tube from a height h so that it may reach the top of the tube? Radius of the tube is R.
The correct answer is:
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Physics
Centre of mass of three particles of masses 1kg, 2 kg and 3kg lies at the point (1,2,3) and centre of mass of another system of particles 3kg and 2kg lies at the point (-1,3,-2). Where should we put a particle of mass 5kg so that the centre of mass of entire system lies at the centre of mass of first system?
Centre of mass of three particles of masses 1kg, 2 kg and 3kg lies at the point (1,2,3) and centre of mass of another system of particles 3kg and 2kg lies at the point (-1,3,-2). Where should we put a particle of mass 5kg so that the centre of mass of entire system lies at the centre of mass of first system?
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A particle is moving in the vertical plane. It is attached at one end of a string of length l whose other end is fixed. The velocity at the lowest point is u. The tension in the string is 
and velocity of the particle is 
at any position. Then, which of the following quantity will remain constant.
A particle is moving in the vertical plane. It is attached at one end of a string of length l whose other end is fixed. The velocity at the lowest point is u. The tension in the string is and velocity of the particle is at any position. Then, which of the following quantity will remain constant.
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A disc (of radius r cm) of uniform thickness and uniform density 
has a square hole with sides of length 
. One corner of the hole is located at the centre of the disc and centre of the hole lies on y-axis as shown. Then the y -coordinate of position of centre of mass of disc with hole (in cm) is
A disc (of radius r cm) of uniform thickness and uniform density has a square hole with sides of length . One corner of the hole is located at the centre of the disc and centre of the hole lies on y-axis as shown. Then the y -coordinate of position of centre of mass of disc with hole (in cm) is
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From the circular disc of radius 4 R two small disc of radius R are cut off. The centre of mass of the new structure will be:
From the circular disc of radius 4 R two small disc of radius R are cut off. The centre of mass of the new structure will be:
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Eight solid uniform cubes of edge l are stacked together to form a single cube with centre O. One cube is removed from this system. Distance of the centre of mass of remaining 7 cubes from O is
Eight solid uniform cubes of edge l are stacked together to form a single cube with centre O. One cube is removed from this system. Distance of the centre of mass of remaining 7 cubes from O is
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A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are
A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are
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Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the origin shown. find the y co-ordinate of the centre of mass of the five-plate system.
Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the origin shown. find the y co-ordinate of the centre of mass of the five-plate system.
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A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.
A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.
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Three particles of masses 
, and 2 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are
Three particles of masses , and 2 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are
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Physics
A small body slides down a smooth uneven surface from a height H, which eventually emerges into a circular loop of radius R(<H) what should be the value of H, so the that force on the body at A is 
times its weight?
A small body slides down a smooth uneven surface from a height H, which eventually emerges into a circular loop of radius R(<H) what should be the value of H, so the that force on the body at A is times its weight?
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Physics
A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball-Earth system remains constant. What is the difference of tension in string at bottom and top during circular motion 
A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball-Earth system remains constant. What is the difference of tension in string at bottom and top during circular motion
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A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating 
is
A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating is
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Three identical particles each of mass 1kg are placed with their centres on a straight line. Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is
Three identical particles each of mass 1kg are placed with their centres on a straight line. Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is
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A weightless rod of length 2l carries two equal masses ‘m’, one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is:
A weightless rod of length 2l carries two equal masses ‘m’, one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is:
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