The potential energy of a particle varies with distance \(r\) as shown in the graph. The force acting on the particle is equal to zero at:
1. \(P\)
2. \(S\)
3. both \(Q\) and \(R\)
4. both \(P\) and \(S\)
A block of mass m is placed in an elevator moving down with an acceleration . The work done by the normal reaction on the block as the elevator moves down through a height h is:
1.
2.
3.
4.
A particle is moving such that the potential energy U varies with position in metre as U (x) = ( - 2x + 50) J. The particle will be in equilibrium at:
1. x = 25 cm
2. x = 2.5 cm
3. x = 25 m
4. x = 2.5 m
The potential energy of a particle of mass 1 kg free to move along the X-axis is given by \(U(x) = (3x^2-4x+6)~\text{J}\). The force acting on the particle at x = 0 will be:
1. 2 N
2. -4 N
3. 5 N
4. 4 N
A particle of mass 'm' is projected at an angle ' with the horizontal, with an initial velocity 'u'. The work done by gravity during the time it reaches its highest point is:
1.
2.
3.
4.
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. \(\frac{F}{\sqrt{2mK}}\)
2. \(\frac{\sqrt{2}F}{\sqrt{mK}}\)
3. \(\frac{F}{\sqrt{mK}}\)
4. \(\frac{2F}{\sqrt{2mK}}\)
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 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.
2.
3. 0
4.
The potential energy \(\mathrm{U}\) of a system is given by (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
4. proportional to
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.