A carpet of mass M and of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a rough floor. The carpet starts unrolling without sliding on the floor where a negligibly small push is given to it. The horizontal velocity of the axis of the cylindrical part of the carpet when its radius reduces to R/2. is then x is :
A thin uniform square plate ABCD of side a and mass m is suspended in vertical plane as shown in the figure. AE and BF are two massless inextensible strings. The line AB is horizontal. Find the tension in the string AE just after BF is cut is 2mg/x , then is :
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A uniform rod of length R and mass M is freely to rotate about a horizontal axis passing through hinge P as is figure. First it is taken aside such that it becomes horizontal and then released. At the lowest point the rod hits the block B of mass m and stops. If ratio of mass of rod M to the mass of block m such that the block B completes the circle then x is. Neglect any friction.
A square plate of edge a/2 is cut out from a uniform square plate of edge a’ as shown in figure. The mass of the remaining portion is M. The moment of inertia of the shaded portion about an axis passing through O (centre of the square of side a and perpendicular to plane of the plate is given by nma2. Find the value of n?
In the figure shown a block B of mass m can slide on a fixed horizontal smooth plane. A uniform solid sphere A of radius r of the same mass rolls without sliding on the block B. Find the angular acceleration of the sphere xg/r then x is :
A billiard ball at rest is struck horizontally one tenth of the diameter below the top. If P be the linear impulse of the blow find the initial kinetic energy of the ball is Then x is given by the mass of the ball is being M.
A uniform rod of length 75 cm hinged at one ends and is free to rotate in vertical plane. It is released from rest when rods is horizontal. When the rod becomes vertical, it is broken at mid-point and lower part now moves freely. The distance of centre of lower part from it again becomes vertical for the first time is r. Find the approximate value of 2r.
Figure shows an arrangement of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass m4, is 48 kg then mass m1 (in kg) is equal to
A solid homogeneous cylinder of height h = 1m and base r = 1m is kept vertically on a conveyor belt moving horizontally with an increasing velocity v = 1 + t2. If the cylinder is not allowed to slip find the time when the cylinder is about to topple.
A small block of mass m is rigid attached at P to a ring of mass 3m and radius r. The system is released from rest at θ = 90° and rolls without sliding. The angular acceleration of hoop just after released is given by ng/r. Find the value of n.