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A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle with the horizontal. The weight experienced by the person is :
(3) W2
[figure]
Weight W acts at the middle; the shoulder pushes up with R. Taking torques about the ground end O (forces at O give no torque):
R L = W L2
R = W2 (independent of )
Answer: (3)
A string is wrapped around the rim of a wheel of moment of inertia 0.40 kgm2 and radius 10 cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N. The angular velocity of the wheel after 10 s is x rad/s, where x is .
A circular disc reaches from top to bottom of an inclined plane of length l. When it slips down the plane, it takes t s. When it rolls down the plane then it takes ( 2 )1/2t s, where is .
A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate is n9. The value of n is . [figure]
A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity . If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is :
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be hours 30 minutes.
Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be kg m2.
Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is 8/x. The value of x is : [figure]
A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x5. The value of x is .
A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v. The sphere and the cylinder reach upto maximum heights h1 and h2 respectively, above the initial level. The ratio h1 : h2 is n10. The value of n is .
In a system two particles of masses m1 = 3 kg and m2 = 2 kg are placed at certain distance from each other. The particle of mass m1 is moved towards the center of mass of the system through a distance 2 cm. In order to keep the center of mass of the system at the original position, the particle of mass m2 should move towards the center of mass by the distance cm.