Q. No.A block of mass \(m\) initially at rest, is dropped from a height \(h\) onto a spring of force constant \(k.\) If the maximum compression in the spring is \(x,\) then:
1. \(m g h = \frac{1}{2} k x^{2}\)
2. \(m g \left(h + x\right) = \frac{1}{2} k x^{2}\)
3. \(m g h = \frac{1}{2} k \left(x + h\right)^{2}\)
4. \(m g \left(h + x \right) = \frac{1}{2} k \left(x + h \right)^{2}\)
1. \(m g h = \frac{1}{2} k x^{2}\)
2. \(m g \left(h + x\right) = \frac{1}{2} k x^{2}\)
3. \(m g h = \frac{1}{2} k \left(x + h\right)^{2}\)
4. \(m g \left(h + x \right) = \frac{1}{2} k \left(x + h \right)^{2}\)
A block of mass \(M\) moving on the frictionless horizontal surface collides with the spring of spring constant \(k\) and compresses it by length \(L.\) The maximum momentum of the block after the collision will be:
| 1. | zero | 2. | \(ML^2 \over k\) |
| 3. | \(\sqrt{Mk}L\) | 4. | \(kL^2 \over 2M\) |
1. \(\dfrac{mv_1t}{t_1}\)
2. \(\dfrac{mv^2_1t}{t_1}\)
3. \(\dfrac{mv_1t^2}{t_1}\)
4. \(\dfrac{mv^2_1t}{t^2_1}\)
A 60 kg man runs up a staircase in 12 seconds while a 50 kg man runs up the same staircase in 11, seconds, the ratio of the rate of doing their work is
(1) 6 : 5
(2) 12 : 11
(3) 11 : 10
(4) 10 : 11
What average horsepower is developed by an 80 kg man while climbing in 10 s a flight of stairs that rises 6 m vertically
(1) 0.63 HP
(2) 1.26 HP
(3) 1.8 HP
(4) 2.1 HP
An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is
(1)
(2)
(3)
(4)
A particle free to move along the x-axis has potential energy given by for , where k is a positive constant of appropriate dimensions. Then
(1) At point away from the origin, the particle is in unstable equilibrium
(2) For any finite non-zero value of x, there is a force directed away from the origin
(3) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin
(4) For small displacements from x = 0, the motion is simple harmonic
The potential energy of a system is represented in the first figure. the force acting on the system will be represented by
(1)
(2)
(3)
(4)
The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig.
The body is in stable equilibrium at
(1) x = x1
(2) x = x2
(3) both x1 and x2
(4) neither x1 nor x2
The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at
(1) C
(2) B
(3) B and C
(4) A and D
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