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
Two springs with spring constants = 1500 N/m and = 3000 N/m are stretched by the same force. The ratio of potential energy stored in the springs will be
1. 2:1
2. 1:2
3. 4:1
4. 1:4
A block of mass 2 kg moving with velocity of 10 m/s on a smooth surface hits a spring of force constant N/m as shown. The maximum compression in the spring is
1. 5 cm
2. 10 cm
3. 15 cm
4. 20 cm
A particle of mass 10 kg is moving with velocity of m/s, where x is displacement . The work done by net force during the displacement of particle from x = 4 to x = 9 m is
1. 1250 J
2. 1000 J
3. 3500 J
4. 2500 J
A particle is moving on the circular path of the radius (R) with centripetal acceleration . Then the correct relation showing power (P) delivered by net force versus time (t) is
1. 1
2. 2
3. 3
4. 4
A body is thrown vertically up with a certain initial velocity. The potential and the kinetic energy of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of the potential and the kinetic energies of the body when it crosses at the same point will be:
1. 1:1
2. 1:4
3. 1:7
4. 1:8
A body is displaced from (0,0) to (1m,1m) along the path x=y by a force . The work done by this force will be :
1.
2.
3.
4.
A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be
1.
2. Fv
3.
4. F/v
A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [ MP PMT 1993]
(1)
(2)
(3)
(4)
Three different objects of mass and m3 are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of:
1.
2.
3. 1 : 1 : 1
4.
A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done by centripetal force in full horizontal circle is
(1) 0
(2)
(3)
(4)
A ball is suspended by a thread of length l. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension:
(1) gl
(2) 2 gl
(3)
(4)
Work done by a frictional force is
(1) Negative
(2) Positive
(3) Zero
(4) All of the above
A block of mass 50 kg slides over a horizontal distance of 1 m. If the coefficient of friction between their surfaces is 0.2, then work done against friction is
(1) 98 J
(2) 72J
(3) 56 J
(4) 34 J
A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is
(1) 0°
(2) 30°
(3) 60°
(4) 90°
A force of Newton acts on a body and displaces it by The work done by the force is
(1) 10 J
(2) 12 J
(3) 16 J
(4) 25 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 potential energy of a body is given by, U = A – Bx2 (Where x is the displacement). The magnitude of force acting on the particle is
(1) Constant
(2) Proportional to x
(3) Proportional to x2
(4) Inversely proportional to x
A 0.5 kg ball is thrown up with an initial speed 14 m/s and reaches a maximum height of 8.0m. How much energy is dissipated by air drag acting on the ball during the ascent
(1) 19.6 Joule
(2) 4.9 Joule
(3) 10 Joule
(4) 9.8 Joule
A particle of mass m at rest is acted upon by a force F for a time t. Its Kinetic energy after an interval t is
(1)
(2)
(3)
(4)
A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. The maximum compression in the spring is x then-
(1)
(2)
(3)
(4)
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
A particle moves from a point to when a force of N is applied. How much work has been done by the force?
1. | 8 J | 2. | 11 J |
3. | 5 J | 4. | 2 J |
A body of mass 1 kg begins to move under the action of a time dependent force \(F = 2 t\) \(\hat{i} + 3 t^{2}\ \hat{j}\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along X and Y axis, What power will be developed by the force at the time (t) ?
(a) \(\left(2 t^{2} + 4 t^{4}\right) W\)
(b) \(\left(2 t^{3} + 3 t^{4}\right) W\)
(c) \(\left(2 t^{3} + 3 t^{5}\right) W\)
(d) \(\left(2 t + 3 t^{3}\right) W\)
Two similar springs P and Q have spring constants KP and KQ, such that KP > KQ. They are stretched, first by the same amount (case a) and then by the same force (case b). The work done by external force, WP and WQ on the springs P and Q in case (a) and case (b) respectively are related as,
1. WP=WQ ; WP>WQ
2. WP=WQ ; WP=WQ
3. WP>WQ ; WQ>WP
4. WP<WQ ; WQ<WP
A block of mass \(10\) kg, moving in the x-direction with a constant speed of \(10\) ms-1, is subjected to a retarding force \(F=0.1x\) J/m during its travel from \(x =20\) m to \(30\) m. Its final kinetic energy will be:
1. | 475 J | 2. | 450 J |
3. | 275 J | 4. | 250 J |
A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest the force on the particle at time t is:
(1)
(2)
(3)
(4)
Two particles of masses m1,m2 move with initial velocities u1 and u2. On collision, one of the particles get excited to higher level, after absorbing energy . If final velocities of particles be v1 and v2, then we must have
(a)m12u1+m22u2-=m12v1+m22v2
(b)m1u12+m2u2=m1v12+m2v22-
(c)m1u12+m2u22-=m1v12+m2v22
(d)m12u12+m22u22+=m12v12+m22v22
A ball is thrown vertically downwards from a height of 20 m with an initial velocity vo. It collides with the ground, loses 50% of its energy in a collision and rebounds to the same height. The initial velocity vo is: (Take g = 10 ms-2)
1. 14 ms-1
2. 20 ms-1
3. 28 ms-1
4. 10 ms-1
A uniform force of (3i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i+k) m to position (4i+3j-k) m. The work done by the force on the particle is-
(1) 9J
(2) 6J
(3) 13J
(4) 15J
A body of mass m is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of the body will be
\(1.~2mgR\)
\(2.~\frac{2}{3}mgR\)
\(3.~3mgR\)
\(4.~\frac{1}{3}mgR\)
The potential energy of a particle in a force field is where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is
(1) B/2A
(2)2A/B
(3)A/B
(4)B/A
A car of mass m starts from rest and
accelerates so that the instantaneous
power delivered to the car has a constant
magnitude . The instantaneous
velocity of this car is proportional to
1. 2.
3. 4.
The potential energy of a system increases if work is done
(1) by the system against a conservative force
(2) by the system against a nonconservative force
(3) upon the system by a conservative force
(4) upon the system by a nonconservative force
A ball moving with velocity collides head on with another stationery ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ) after collision will be
(1)0,1
(2)1,1
(3)1,0.5
(4)0,2
An engine pumps water through a hosepipe. Water passes through the pipe and leaves it with a velocity of 2 The mass per unit length of water in the pipe is 100 What is the power of the engine?
1. 400 W
2. 200 W
3. 100 W
4. 800 W
A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is
(1)
(2)
(3)
(4)
A body of mass 1 kg is thrown upwards with a velocity It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?
(a) 20 J (b) 30 J
(c) 40 J (d) 10 J
A block of mass M is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of k. The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:
1. | Mg/k | 2. | 2Mg/k |
3. | 4 Mg/k | 4. | Mg/2k |
Water falls from a height of 60m at the rate of 15kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (g=10 m/)
1. 8.1 kW 2. 10.2 kW
3. 12.3 kW 4. 7.0 kW
A body of mass moving with uniform velocity of 40 m/s collides with another mass at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses is
(1) 0.75
(2) 1.33
(3) 3.0
(4) 4.0
A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of initial energy transferred to the heavier ball is
(1)
(2)
(3)
(4)
A sphere of mass m moving horizontally with velocity collides against a pendulum bob of mass m. If the two masses stick together after the collision, then the maximum height attained is
(1)
(2)
(3)
(4)
If a body of mass m moving with velocity u collides head-on elastically with another identical body at rest. After collision , velocity of the second body will be
(1) zero
(2) u
(3) 2u
(4) data insufficient
A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is
(a)
(b)
(c)
(d)