Work, Energy and Power

The potential energy function (in J) of a particle in a region of space is given as U= (2x2+3y3+2z ). Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point P(1,2,3) m is :

1. 4
2. 2
3. 8
4. 6

A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies (K.E)A(K.E)B is : [figure]

1. 5 : 1
2. 3 : 2
3. 1 : 5
4. 2 : 5

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10\% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g=10 m s-2]

1. 5 6 m s-1
2. 5 5 m s-1
3. 2 5 m s-1
4. 6 5 m s-1

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

1. 3:5
2. 5:4
3. 2:5
4. 4:5

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ( ) of thread deflection in the extreme position will be :

1. -1 ( 12 )
2. 2 -1 ( 12 )
3. 2 -1 ( 1 5 )
4. -1 ( 2 )