What is the work done by the gravitational force on block \(A\) during the first \(2\) s after the blocks are released? (assume the pulley is light)

               

1. \( 240 ~\text J\)
2. \( 200 ~\text J\)
3. \(120 ~\text J\)
4. \( 24 ~\text J\)

A weight 'mg' is suspended from a spring. The energy stored in the spring is U. The elongation in the spring is:

1.  $\frac{2\mathrm{U}}{\mathrm{mg}}$

2.  $\frac{\mathrm{U}}{\mathrm{mg}}$

3.  $\frac{\sqrt{2}\mathrm{U}}{\mathrm{mg}}$

4.  $\frac{\mathrm{U}}{\sqrt{2}\mathrm{mg}}$

      
1. \(50~\text{J}\)
2. \(100~\text{J}\)
3. \(25~\text{J}\)
4. Zero

A block is carried slowly up an inclined plane. If \(W_f\) is work done by the friction, \(W_N\)${\mathrm{}}_{}$ is work done by the reaction force, \(W_g\) is work done by the gravitational force, and \(W_{ex}\) is the work done by an external force, then choose the correct relation(s):
1. \(W _N +   W _f   +   W _g   +   W _{ex}   =   0\)
2. \(W _N   =   0\)
3. \(   W _f   +   W _{ex}   =    - W _g\)
4. All of these

The principle of conservation of energy implies that:

1.  the total mechanical energy is conserved.

2.  the total kinetic energy is conserved.

3.  the total potential energy is conserved.

4.  the sum of all types of energies is conserved.

The potential energy \(\mathrm{U}\) of a system is given by $\mathrm{U}=$ $\mathrm{A}$ $-$ ${\mathrm{Bx}}^2$ (where \(\mathrm{x}\) is the position of its particle and \(\mathrm{A},\) \(\mathrm{B}\) are constants). The magnitude of the force acting on the particle is:
1. constant

2. proportional to \(\mathrm{x}\)

3. proportional to ${\mathrm{x}}^2$

4. proportional to $\left(\frac{1}{\mathrm{x}}\right)$

A person-1 stands on an elevator moving with an initial velocity of 'v' & upward acceleration 'a'. Another person-2 of the same mass m as person-1 is standing on the same elevator. The work done by the lift on the person-1 as observed by person-2 in time 't' is:

1.  $\mathrm{m}\left(\mathrm{g}\right)$ $+$ $\mathrm{a}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

2.  $-\mathrm{mg}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

3.  0

4.  $\mathrm{ma}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

The figure shows the potential energy function U(x) for a system in which a particle is in a one-dimensional motion. What is the direction of the force when the particle is in region AB? (symbols have their usual meanings)

1.  The positive direction of x

2.  The negative direction of X

3.  Force is zero, so direction not defined

4.  The negative direction of y

A block of mass \(m\) is connected to a spring of force constant \(K.\) Initially, the block is at rest and the spring is relaxed. A constant force \(F\) is applied horizontally towards the right. The maximum speed of the block will be:

                         
1. \(\dfrac{F}{\sqrt{2mK}}\)

2. \(\dfrac{\sqrt{2}F}{\sqrt{mK}}\)

3. \(\dfrac{F}{\sqrt{mK}}\)

4. \(\dfrac{2F}{\sqrt{2mK}}\)