1. Which of the following quantities is conserved in an isolated system with no external force?
Correct Answer: (b) Linear Momentum
In an isolated system with no external forces, linear momentum is always conserved according to Newton's first law. While energy is conserved in general, it can transform between different forms (kinetic to potential, etc.), so specific forms aren't necessarily conserved.
2. What is the primary reason that a rocket can move in space where there is no atmosphere?
Correct Answer: (d) Newton's third law
Rockets work by expelling gas downward (action), which creates an equal and opposite force upward (reaction) on the rocket according to Newton's third law. While momentum is conserved in the system, the direct cause of motion is the action-reaction pair.
3. A jet plane flies in the air because
Correct Answer: (c) The flow of air around the wings causes an upward force, which compensates for the force of gravity
Jet planes fly due to lift generated by the flow of air over their wings (Bernoulli's principle). The shape of the wings causes faster airflow over the top surface, creating lower pressure above than below, resulting in upward lift.
4. If a force of 250 N acts on body, the momentum acquired is 125 kg-m/s. What is the period for which force acts on the body?
Correct Answer: (a) 0.5 sec
Using the impulse-momentum theorem: \( F \times t = \Delta p \)
\( t = \frac{\Delta p}{F} = \frac{125}{250} = 0.5 \) sec
\( t = \frac{\Delta p}{F} = \frac{125}{250} = 0.5 \) sec
5. A player caught a cricket ball of mass 150 gm moving at a rate of 20 m/s. If the catching process be completed in 0.1 s, then the force of the blow exerted by the ball on the hands of the player is
Correct Answer: (b) 30 N
First convert mass to kg: 150 gm = 0.15 kg
Change in momentum: \( \Delta p = m \times v = 0.15 \times 20 = 3 \) kg-m/s
Force: \( F = \frac{\Delta p}{t} = \frac{3}{0.1} = 30 \) N
Change in momentum: \( \Delta p = m \times v = 0.15 \times 20 = 3 \) kg-m/s
Force: \( F = \frac{\Delta p}{t} = \frac{3}{0.1} = 30 \) N
6. A rocket has a mass of 100 kg. 90% of this is fuel. It ejects fuel vapours at the rate of 1 kg/sec with a velocity of 500 m/sec relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is
Correct Answer: (b) 500 N
Thrust force is given by: \( F = v_{rel} \times \frac{dm}{dt} \)
\( F = 500 \times 1 = 500 \) N
\( F = 500 \times 1 = 500 \) N
7. In which of the following cases forces may not be required to keep the
Correct Answer: (b) Particle going along a straight line
According to Newton's first law, no force is needed to maintain motion at constant velocity (straight line motion). All other cases require force - circular motion needs centripetal force, changing momentum requires force, and maintaining acceleration requires continuous force.
8. A wagon weighing 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is
Correct Answer: (c) 40 km/hour
Using conservation of momentum: \( m_1v_1 = (m_1 + m_2)v_2 \)
\( 1000 \times 50 = (1000 + 250) \times v_2 \)
\( v_2 = \frac{50000}{1250} = 40 \) km/hour
\( 1000 \times 50 = (1000 + 250) \times v_2 \)
\( v_2 = \frac{50000}{1250} = 40 \) km/hour
9. During a collision, if total kinetic energy is not conserved but total momentum is, the collision is:
Correct Answer: (b) Inelastic
Inelastic collisions conserve momentum but not kinetic energy (some energy is converted to other forms like heat or sound). Perfectly elastic collisions conserve both momentum and kinetic energy.
10. A ball is thrown at a wall and bounces back with less speed. Which of the following best explains this phenomenon?
Correct Answer: (a) Linear momentum is conserved, but energy is lost as heat/sound
The system (ball + wall + Earth) conserves momentum, but the ball loses kinetic energy which is converted to heat and sound during the collision. This is characteristic of inelastic collisions.
11. A 100 g iron ball having velocity 10 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the wall is
Correct Answer: (a) 10 N
Only the perpendicular component changes: \( v_{\perp} = 10 \times \cos(30°) \)
Change in momentum: \( \Delta p = 2 \times m \times v_{\perp} = 2 \times 0.1 \times 10 \times \frac{\sqrt{3}}{2} \approx 1.732 \) kg-m/s
Force: \( F = \frac{\Delta p}{t} = \frac{1.732}{0.1} \approx 17.32 \) N (Note: There seems to be discrepancy with given options)
Change in momentum: \( \Delta p = 2 \times m \times v_{\perp} = 2 \times 0.1 \times 10 \times \frac{\sqrt{3}}{2} \approx 1.732 \) kg-m/s
Force: \( F = \frac{\Delta p}{t} = \frac{1.732}{0.1} \approx 17.32 \) N (Note: There seems to be discrepancy with given options)
12. A car and a truck collide and stick together. To assess whether linear momentum is conserved, what must be true?
Correct Answer: (c) No external horizontal force acts on the system
Momentum is conserved when the net external force on a system is zero. For horizontal momentum conservation during collision, there must be no external horizontal forces acting on the car-truck system.
13. A ball of mass 150g starts moving with an acceleration of 20 m/s² when hit by a force, which acts on it for 0.1 sec. The impulsive force is
Correct Answer: (c) 0.3 N-s
First convert mass to kg: 150g = 0.15 kg
Force: \( F = m \times a = 0.15 \times 20 = 3 \) N
Impulse: \( J = F \times t = 3 \times 0.1 = 0.3 \) N-s
Force: \( F = m \times a = 0.15 \times 20 = 3 \) N
Impulse: \( J = F \times t = 3 \times 0.1 = 0.3 \) N-s
14. A body, whose momentum is constant, must have constant
Correct Answer: (b) Velocity
Momentum \( p = mv \). If momentum is constant and mass doesn't change, then velocity must be constant. Constant velocity means zero acceleration (F=ma=0).
15. The motion of a rocket is based on the principle of conservation of
Correct Answer: (c) Linear momentum
Rockets work by expelling mass (fuel) backward, gaining forward momentum to conserve the total momentum of the system (rocket + exhaust gases).
16. A rope of length 5m is kept on frictionless surface and a force of 5N is applied to one of its end. Find tension in the rope at 1m from this end
Correct Answer: (c) 4 N
Mass distribution is uniform (1m segment has 1/5 of total mass). Acceleration \( a = F/m \). For 4m segment (opposite side): \( T = m_{segment} \times a = (4/5)m \times (5/m) = 4 \) N
17. An aircraft is moving with a velocity of 500 m/s. If all the forces acting on it are balanced, then
Correct Answer: (a) It still moves with the same velocity
Balanced forces mean zero net force (F=0). From Newton's first law, an object in motion stays in motion with constant velocity when F=0.
18. A rocket of mass 1000 kg exhausts gases at a rate of 4 kg/sec with a velocity 3000 m/s. The thrust developed on the rocket is
Correct Answer: (a) 12000 N
Thrust \( F = v_{rel} \times \frac{dm}{dt} = 3000 \times 4 = 12000 \) N
19. The momentum is most closely related to
Correct Answer: (b) Impulse
Impulse is defined as change in momentum (\( J = \Delta p \)). Force is related through \( F = dp/dt \), but impulse is directly equal to momentum change.
20. Rocket engines lift a rocket from the earth surface because hot gas with high velocity
Correct Answer: (c) React against the rocket and push it up
According to Newton's third law, the action of expelling gases downward creates a reaction force upward on the rocket. This works even in vacuum (no air to push against).
21. A man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of one kg mass. by what velocity the gun rebounds backwards
Correct Answer: (c) 1 m/s
Using conservation of momentum: \( m_bv_b = m_gv_g \)
\( 0.2 \times 5 = 1 \times v_g \) ⇒ \( v_g = 1 \) m/s
\( 0.2 \times 5 = 1 \times v_g \) ⇒ \( v_g = 1 \) m/s
22. A bullet of mass 5 g is shot from a gun of mass 5 kg. The muzzle velocity of the bullet is 500 m/s. The recoil velocity of the gun is
Correct Answer: (a) 0.5 m/s
Using conservation of momentum: \( m_bv_b = m_gv_g \)
\( 0.005 \times 500 = 5 \times v_g \) ⇒ \( v_g = 0.5 \) m/s
\( 0.005 \times 500 = 5 \times v_g \) ⇒ \( v_g = 0.5 \) m/s
23. A ball of mass 2 kg hits a wall with velocity 10 m/s and rebounds with velocity 8 m/s. What is the impulse delivered by the wall?
Correct Answer: (c) 36 Ns
Impulse \( J = \Delta p = m(v_f - v_i) = 2(8 - (-10)) = 2 \times 18 = 36 \) Ns
Note: Direction change means we consider -10 m/s for initial velocity when rebounding at +8 m/s
Note: Direction change means we consider -10 m/s for initial velocity when rebounding at +8 m/s
24. Two ice skaters push off each other on a frictionless surface. Skater A is heavier than Skater B. Which statement is true about their momenta after the push?
Correct Answer: (b) Both have the same magnitude of momentum
By Newton's third law, the forces are equal and opposite, and act for the same time, so impulses (Δp) are equal in magnitude but opposite in direction. Thus momenta are equal in magnitude.
25. A force of 50 dynes is acted on a body of mass 5 g which is at rest for an interval of 3 seconds, then impulse is
Correct Answer: (a) 150 dyne-s
Impulse \( J = F \times t = 50 \times 3 = 150 \) dyne-s
26. A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of
Correct Answer: (c) 2.5 m/s
Mass of third piece: \( M - \frac{M}{4} - \frac{M}{4} = \frac{M}{2} \)
Momentum vectors at right angles: \( p_{total} = \sqrt{(3M/4)^2 + (4M/4)^2} = 5M/4 \)
\( \frac{M}{2}v = \frac{5M}{4} \) ⇒ \( v = 2.5 \) m/s
Momentum vectors at right angles: \( p_{total} = \sqrt{(3M/4)^2 + (4M/4)^2} = 5M/4 \)
\( \frac{M}{2}v = \frac{5M}{4} \) ⇒ \( v = 2.5 \) m/s
27. The momentum of a system is conserved
Correct Answer: (c) In the absence of an external force on the system
Momentum is conserved when the net external force on a system is zero (isolated system). Internal forces can redistribute momentum within the system but don't change the total momentum.
28. A body of mass 0.25 kg is projected with muzzle velocity 100 m/s from a tank of mass 100 kg. What is the recoil velocity of the tank
Correct Answer: (a) 0.25 m/s
Using conservation of momentum: \( m_pv_p = m_tv_t \)
\( 0.25 \times 100 = 100 \times v_t \) ⇒ \( v_t = 0.25 \) m/s
\( 0.25 \times 100 = 100 \times v_t \) ⇒ \( v_t = 0.25 \) m/s
29. A bullet is fired from a gun. The force on the bullet is given by \( F = 600 - 2 \times 10^5 t \) newtons, where t is in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet
Correct Answer: (c) 0.9 Ns
First find when F=0: \( 600 - 2 \times 10^5 t = 0 \) ⇒ \( t = 0.003 \) s
Impulse is integral of F dt: \( \int_0^{0.003} (600 - 2 \times 10^5 t) dt = 600t - 10^5 t^2 \big|_0^{0.003} = 1.8 - 0.9 = 0.9 \) Ns
Impulse is integral of F dt: \( \int_0^{0.003} (600 - 2 \times 10^5 t) dt = 600t - 10^5 t^2 \big|_0^{0.003} = 1.8 - 0.9 = 0.9 \) Ns
30. A bullet of mass 0.1 kg is fired with a speed of 100 m/s, the mass of gun is 50 kg. The velocity of recoil is
Correct Answer: (a) 0.2 m/s
Using conservation of momentum: \( m_bv_b = m_gv_g \)
\( 0.1 \times 100 = 50 \times v_g \) ⇒ \( v_g = 0.2 \) m/s
\( 0.1 \times 100 = 50 \times v_g \) ⇒ \( v_g = 0.2 \) m/s
31. You are tasked with designing a bumper that reduces injury during a car crash. Which of the following physical principles should guide your design?
Correct Answer: (a) Increase the time of collision to reduce force (Impulse = Ft)
From the impulse-momentum theorem (\( J = \Delta p = F \times t \)), increasing collision time reduces the average force experienced for a given momentum change, which reduces injury.
32. A student wants to test conservation of momentum using air track gliders. Which setup would best demonstrate the principle?
Correct Answer: (b) Use two gliders with unequal mass and measure their velocities before and after collision
Conservation of momentum is best demonstrated by measuring total momentum before and after a collision between two objects. Using unequal masses makes the effect more noticeable.
33. A bullet mass 10 gm is fired from a gun of mass 1kg. If the recoil velocity is 5 m/s, the velocity of the muzzle is
Correct Answer: (d) 500 m/s
Using conservation of momentum: \( m_gv_g = m_bv_b \)
\( 1 \times 5 = 0.01 \times v_b \) ⇒ \( v_b = 500 \) m/s
\( 1 \times 5 = 0.01 \times v_b \) ⇒ \( v_b = 500 \) m/s
34. A rocket can go vertically upwards in earth's atmosphere because
Correct Answer: (d) Of the force exerted on the rocket by gases ejected by it
Rockets move upward due to the reaction force from the high-speed ejection of exhaust gases downward (Newton's third law), not by pushing against air.
35. At a certain instant of time the mass of a rocket going up vertically is 100 kg. If it is ejecting 5 kg of gas per second at a speed of 400 m/s, the acceleration of the rocket would be (taking g = 10 m/s²)
Correct Answer: (a) 10 m/s²
Thrust \( F = v_{rel} \times \frac{dm}{dt} = 400 \times 5 = 2000 \) N
Net force \( F_{net} = F - mg = 2000 - (100 \times 10) = 1000 \) N
Acceleration \( a = F_{net}/m = 1000/100 = 10 \) m/s²
Net force \( F_{net} = F - mg = 2000 - (100 \times 10) = 1000 \) N
Acceleration \( a = F_{net}/m = 1000/100 = 10 \) m/s²
36. A jet engine works on the principle of
Correct Answer: (c) Conservation of linear momentum
Jet engines accelerate air backward, creating forward thrust due to momentum conservation. The action (air backward) produces reaction (engine forward).
37. A gun of mass 5 kg fires a bullet of mass 0.05 kg with a velocity of 200 m/s. What is the recoil velocity of the gun?
Correct Answer: (b) -2 m/s
Using conservation of momentum: \( m_bv_b + m_gv_g = 0 \)
\( 0.05 \times 200 + 5 \times v_g = 0 \) ⇒ \( v_g = -2 \) m/s
\( 0.05 \times 200 + 5 \times v_g = 0 \) ⇒ \( v_g = -2 \) m/s
38. When two objects collide and stick together, what type of collision has occurred?
Correct Answer: (b) Inelastic collision
In an inelastic collision, objects stick together after impact, and kinetic energy is not conserved (though momentum is). This is distinct from elastic collisions where both momentum and kinetic energy are conserved.
39. A 2 kg object moving at 3 m/s collides with a stationary 4 kg object. If they stick together, what is their final velocity?
Correct Answer: (b) 1.0 m/s
Using conservation of momentum: \( m_1v_1 + m_2v_2 = (m_1 + m_2)v_f \)
\( (2 \times 3) + (4 \times 0) = (2 + 4)v_f \)
\( 6 = 6v_f \) ⇒ \( v_f = 1 \) m/s
\( (2 \times 3) + (4 \times 0) = (2 + 4)v_f \)
\( 6 = 6v_f \) ⇒ \( v_f = 1 \) m/s
40. Which of the following best illustrates Newton's third law?
Correct Answer: (c) A swimmer pushing water backward and moving forward
Newton's third law states that for every action there is an equal and opposite reaction. When the swimmer pushes water backward (action), the water pushes the swimmer forward (reaction). This clearly shows action-reaction pairs.