A frictionless track ends in a circular loop of radius . A body slides down the track from point which is it height . Maximum value of for the body to successfully complete the loop is

Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is

Domain of definition of the function, is

If represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between

Given below is a graph between a variable force (along -axis) and the displacement (along -axis) of a particle in one dimension. The work done by the force in the displacement interval between and is

A particle of mass moving with a velocity makes an elastic one dimensional collision with a stationary particle of mass establishing a contact with it for extremely small time . Their force of contact increases from zero to linearly in time , remains constant for a further time and decreases linearly from to zero in further time as shown. The magnitude possessed by is

Let be a set containing 10 distinct elements, then the total number of distinct functions from to is-

The domain is defined as the set which is to input in a function. We say that input values satisfy a function. The range is defined as the actual output supposed to be obtained by entering the domain of the function.
Co-domain is defined as the values that are present in the right set that is set Y, possible values expected to come out after entering domain values.

The number of bijective functions from set A to itself when a contains 106 elements-

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of is

A particle is acted upon by a force which varies with position as shown in figure. If the particle at has kinetic energy of 25 J, then the kinetic energy of the particle at is

A vertical spring with force constant is fixed on a table. A ball of mass at a height above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance . The net work done in the process is

Figure shows the -graph. Where is the force applied and is the distance covered

By the body along a straight line path. Given that is in and in , what is the work done?

Range of function f(x) = , is given by -

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses and . Taking , find the work done (in joules) by the string on the block of mass during the first second after the system is released from rest

An object of mass is tied to a string of length and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angel with the vertical. Work done by the force is

A block of mass kg sliding on a smooth horizontal surface with a velocity meets the spring of spring constant fixed at one end as shown in figure. The maximum compression of the spring and velocity of block as is returns to the original position respectively are