A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is
1. 84J
2. 68J
3. 23J
4. 8J
In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The minimum speed at highest point of track will be
(1)
(2) 2gR
(3)
(4)
A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table?
(1) 7.2 J
(2) 3.6 J
(3) 120 J
(4) 1200 J
A mass of 0.5kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be
(1) 0.15 m
(2) 0.12 m
(3) 1.5 m
(4) 0.5 m
The spring extends by x on loading, then energy stored by the spring is : (if T is the tension in spring and k is spring constant)
(1)
(2)
(3)
(4)
A particle of mass 'm' is moving in a horizontal circle of radius 'r' under a centripetal force equal to –K/r2, where K is a constant. The total energy of the particle will be:
1.
2.
3.
4.
A force \(F = -k(y\hat i +x\hat j)\) (where \(k\) is a positive constant) acts on a particle moving in the \(xy\text-\)plane. Starting from the origin, the particle is taken along the positive \(x\text-\)axis to the point \((a,0)\) and then parallel to the \(y\text-\)axis to the point \((a,a)\). The total work done by the force on the particle is:
1. \(-2ka^2\)
2. \(2ka^2\)
3. \(-ka^2\)
4. \(ka^2\)
The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:
1. \(4U\)
2. \(8U\)
3. \(16U\)
4. \(U/4\)
A body of mass 0.5 kg thrown vertically upward with 20 m/s reaches a maximum height of 16 m. The amount of energy dissipated by the air drag acting on the ball during the ascent is:
1. 20 J
2. 10 J
3. 4 J
4. 8 J
What is the work done by gravity on block A in 2 seconds after the blocks are released? (Pulley is light)
1. 240 J
2. 200 J
3. 120 J
4. 24 J
Work done in time t on a body of mass m, when it is accelerated from rest with constant acceleration to a speed v in time , as a function of time t is given by:
1.
2.
3.
4.
In the case of collision (one dimension or two dimensions):-
1. Momentum remains conserved and total energy not
2. Momentum and total energy both are conserved
3. Momentum is not conserved and total energy remains conserved
4. Momentum and total energy both are not conserved
Two vehicles are moving with the same kinetic energy. If the ratio of their masses is 1 : 3 then find the ratio of their stopping distances when both vehicles stop with the same retardation.
(1) 1: 1
(2) 3: 1
(3) 9: 1
(4) 1: 9
An object of mass \(m=1.5\) kg is acted upon by the force as shown in the figure that varies with the position of the object as shown. If the object starts from rest at a point \(x =0,\) then what is its speed at \(x = 50\) m?
1. \(20\) m/s
2. \(25\) m/s
3. \(15\) m/s
4. \(17\) m/s
A particle is moving along the x-axis under a conservative force and its potential energy U varies with x co-ordinate as shown in the figure. Then force is positive at:
(1) A
(2) C, D
(3) B
(4) D, E
A body A of mass 10 kg at rest starts slipping from the top of the inclined plane of height 10 m as shown. If it reaches the ground at 10 m/s, then work done by friction is
(1) 500 J
(2) -500 J
(3) 1000 J
(4) -1000 J
A particle of mass m is pressed against a spring of spring constant k, through a compression x. It is released suddenly speed of the particle, when it separates from the spring is
1.
2.
3.
4.
The ratio of velocities of a body connected to a string at points A, B and C to just complete vertical circular motion is:
(1) 1: 2: 3
(2)
(3) 1: 3: 5
(4)
A body at rest is released from height h on a frictionless track which leads to a vertical circle as shown in the figure. If the body just completes the vertical circle, the relation between R and h is
1.
2. h = 2R
3.
4.
A particle of mass \(1\) kg starts from origin under the force as shown by the graph. The velocity of the particle at \(x =2\) m is:
1. \(\sqrt{40}\) m/s
2. \(\sqrt{20}\) m/s
3. \(\sqrt{10}\) m/s
4. \(40\) m/s
Position-time graph of a particle of mass 2 kg is shown in the figure. Total work done on the particle from t=0 to t=4s is:
1. 8 J
2. 4 J
3. 0 J
4. can't be determine
In a nuclear reactor, a neutron of high speed (typically \(\left(10\right)^{7}\) m/s) must be slowed to \(\left(10\right)^{3}\) m/s so that it can have a high probability of interacting with isotope \(^{235}_{92}U\) and causing it to fission. The material making up the light nuclei, usually heavy water \(\left(D_{2} O\right)\) or graphite, is called a moderator. Find the fraction of the kinetic energy of the neutron lost by it in an elastic collision with light nuclei like deuterium.
1. \(\dfrac{1}{9}\)
2. \(\dfrac{8}{9}\)
3. \(\dfrac{9}{8}\)
4. \(\dfrac{1}{8}\)
A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled \(3~\text{m}\) is:
1. \(2.5~\text{J}\)
2. \(6.5~\text{J}\)
3. \(4~\text{J}\)
4. \(5~\text{J}\)
(a) | The spring was initially compressed by a distance \(x\) and was finally in its natural length. |
(b) | It was initially stretched by a distance of \(x\) and finally was in its natural length. |
(c) | It was initially in its natural length and finally in the compressed position. |
(d) | It was initially in its natural length and finally in a stretched position. |
Choose the correct option from the given ones:
1. | (a) and (b) only |
2. | (b) and (c) only |
3. | (c) and (d) only |
4. | (a), (b), (c), (d) |
A rod of mass \(M\) and length \(L\) is suspended vertically at its highest point. The rod is held such that it is horizontal and free to rotate about A and then released. There is no friction anywhere.
The kinetic energy of the rod, when it reaches the lowest position, is:
1. | \(MgL\) | 2. | \(\dfrac{MgL}{2}\) |
3. | \(\dfrac{2}{3}MgL\) | 4. | \(\dfrac{MgL}{12}\) |
1. | \(2\sqrt{10}\) ms–1 | 2. | \(2\sqrt{5}\) ms–1 |
3. | \(4\sqrt{10}\) ms–1 | 4. | \(4\sqrt{5}\) ms–1 |