An object is falling freely under the gravitational force. Its velocity after travelling a distance h is v. If v depend upon gravitational acceleration g and distance h, prove with dimensional analysis `v = k ` sqrt(gh)`, where k is constant.

A body falls freely under gravity. Its speed is v when it has lost an amount U of the gravitational energy. Then its mass is

If the velocity of a particle is v = At + Bt^2 . where A and B are constants, then the distance travelled by it between 1 s and 2 s is

A point object moves along an arc of a circle or radius'R' . Its velocity depends upon the distance covered 'S' as V=KsqrtS Where'K' is a constant. IF theta is the angle between the total acceleration and tangential accleration , then

A particle is executing a linear S.H.M. Its velocity at a distance x from the mean position is given by v^2=144-9x^2 . The maximum velocity of the particle is

Consider a small sphere falling through a medium. The viscous force acting on the sphere depends upon the radius (r) of the sphere, velocity (V) of the sphere and the co-efficient of viscosity (eta) of the medium. Use dimensional analysis and show that the viscous force is directly proportional to etarv . (Given : Dimensions of eta =[M^1L^-1T^-1]) .

Select the appropriate options and complete the following paragraph (Velocity, independent, initial velocity, dependent, gravity, friction, final velocity , direction ) The motion of any object under the influence of the force of ______ alone is called as free fall. During free fall, there will be no change in the ______ of motion of the object. But there will be a change in the magnitude of ______ of the object due to the gravitational pull of the earth . The acceleration that an object experiences during free fall is ____ of the mass of the object undergoing motion. when a body is dropped freely from a height, its ______ is zero. Whereas when a body is thrown vertically upwards, its ________ is zero .

Kepler's third law states that square of period revolution (T) of a planet around the sun is proportional to third power of average distance i between sun and planet i.e. T^(2)=Kr^(3) here K is constant if the mass of sun and planet are M and m respectively then as per Newton's law of gravitational the force of alteaction between them is F=(GMm)/(r^(2)) , here G is gravitational constant. The relation between G and K is described as

A metallic ring of mass m and radius i (ring being horizontal) is falling under gravity in a region having a magnetic field . If z is the vertical direction, the z- component of magnetic field is B_z = B_0(1 + lambda z) If R is the resistance of the ring and if the ring falls with a velocity v, find the power lost in the resistance . If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B , lambda and acceleration due to gravity g.

A body of mass m starts moving from a position of rest with a constant acceleration a. After covering a distance, it has acquired velocity v. What will be the magnitude of its velocity after it has covered a distance 2s?

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x gt0 ) v prop(1)/(sqrt(x)) . Find how the magnitude of the force (F) on the particle depends on x.