Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10 ):

A collar 'B' of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5m. The spring lying in the plane of the circular track and having spring constant 200 is undeformed when the collar is at 'A'. If the collar starts from rest at B' the normal reaction exerted by the track on the collar when it passes through 'A' is:

The blocks A and B shown in the figure have masses . The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is:

Two bodies of mass are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull with constant velocity v is:

A small block slides with velocity on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle q in the figure is:

A bob hangs from a rigid support by an inextensible string of length If it is displaced through a distance (from the lowest position) keeping the string straight & released, the speed of the bob at the lowest position is:

The angle of rotation of the axes so that the equation may be reduced to the form

By translation of axes the equation  C=

In the adjoining figure AB = 14 units, BC = 12 units and BD = 13 units. Find the value of sec

Glycerol has:

In the figure shown, the system is released from rest. Find the velocity of block m m A B P A when block B has fallen a distance '. Assume all pulleys to be massless and frictionless.

A block of mass m is attached to two spring of spring constant as shown in figure. The block is displaced by x towards right and released. The velocity of the block when it is at will be :

Hence answer is isinx

A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force F can do is : [Given that spring does not break]

The given plot shows the variation, the potential energy (U) of interaction between two particles with the separating distance (r) between them. Which of the above statements are correct?

1) B and D are equilibrium points
2) C is a point of stable equilibrium points
3) The force of interaction between the two particles is attractive between points C and D and repulsive between points D and E on the curve

In the figure shown the potential energy (U) of a particle is plotted against its position 'x' from origin. Then which of the following statement is correct. A particle at :