Systems of Part...

One end of a uniform rod of length l and mass m is hinged at A. It is released from rest from horizontal position AB as shown in Fig. The force exerted by the rod on the hinge when it becomes vertical is

A uniform rod of mass m and length l is suspended by means of two light inextensible strings as shown in Fig. Tension in one string immediately after the other string is cut is

A force F is applied at the top of a ring of mass M and radius R placed on a rough horizontal surface as shown in Fig. Friction is sufficient to prevent slipping. The frictional force acting on the ring is

A rectangular block has a square base measuring a × a, and its height is h. It moves on a horizontal surface in a direction perpendicular to one of its edges. The coeffiient of friction is μ. It will topple if

The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to circumference of disc and parallel to its diameter is

An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A, Fig. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and other along AC. Neglecting frictional effects, the quantities that are conserved as the beads slide down are

A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O, as shown in Fig. The moment of inertia of the loop about the axis XX’ is

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ω₀. When the tortoise moves along a chord of the platform with a constant velocity (w.r.t. the platform), the angular velocity of the platform will vary with the time t as

Two spherical bodies of masses M and 5 M and radii R and 2 R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm as shown in Fig. The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm² will be