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Q1. If we apply Newton's First Law to torque then the statement will be

• If the net torque acting on a rigid object is zero, it will rotate with a non-uniform angular velocity.
• If the net torque acting on a rigid object is non zero, it will rotate with a non-uniform angular velocity.
• If the net torque acting on a rigid object is zero, it will rotate with a constant angular velocity.
• If the net torque acting on a rigid object is non zero, it will rotate with a constant angular velocity.

Solution

If the net torque acting on a rigid object is zero, it will rotate with a constant angular velocity.

Q2. A ring is rolling on a horizontal surface without slipping. Find the ratio of translation K.E. to rotational K.E. of ring.

• 1 : 1
• 1 : 2
• 2 : 1
• 4 : 1

Solution

Q3. Two bodies of masses m1 and m2 are moving such that their momentums are equal and opposite. The velocity of centre of mass of system of two bodies is:

• Zero
• equal to the velocity of particle m1.
• equal to the velocity of particle m2.
• cannot be determined.

Solution

Q4. A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and center of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ωA and ωB respectively. Then

• ω_A< ω_B
• ω_A = ω_B
• ω_A = ω
• ω_B = ω

Solution

Since there is no friction between the sphere and horizontal surface and also between the spheres themselves, there will be no transfer of angular momentum from sphere A to sphere B due to collision.Since the collision is elastic and the spheres have same mass,the sphere A only transfers its linear velocity v to the sphere B.Sphere A will continue to rotate with the same angular speed ω at a fixed location. 

Q5. A stick is thrown in the air and lands on the ground at same distance from the thrower. The centre of mass of the stick will move along a parabolic path

• in all cases
• only if the stick has linear motion but no rotational motion
• only if the stick is uniform
• only if the stick has a shape such that its centre of mass is located at same point on it and not outside

Solution

In all the cases given the centre of mass of the stick will move along a parabolic path.

Q6. A rigid body is said to be in mechanical equilibrium if

• net force on the rigid body is zero
• net torque on the rigid body is zero
• either net force or net torque on the rigid body is zero
• both net force and net torque on the rigid body is zero

Solution

The necessary condition for a rigid body to be in equilibrium is that: The resultant of all the external forces must be zero. The resultant of all the external torques must be zero.

Q7. Angular momentum is equal to____.(All the symbols used have their usual meanings)

• L = I²ω
• L = ma
• L = I/α
• L = Iω

Solution

L = Iω You know that linear momentum p = mv and moment of inertia I is analogus to mass m in momentum. Angular velocity ω is analogus to linear velocity v in linear momentum.

Q8. Which of the following is not a binary system?

• Diatomic molecule
• Earth-Moon system
• Binary stars
• Earth-Moon-Sun system

Solution

A binary system is one in which two bodies revolve about a common centre of mass. In Earth-Moon-Sun system, center of mass lies in the Sun. So, it is not consider as a binary system.

Q9. Vectorially, angular velocity of a rotating body is represented :

• along the radius towards the centre.
• along the radius away from the centre
• along the axis of rotation
• none of the above

Solution

Vectorially, angular velocity of a rotating body is represented along the axis of rotation.

Q10. What is the relation between rad/s ²  and r p s ²  ?

•  2π rps²  = 1 rad/s² 
• 1rps²  =  2π rad/s² 
• 2/π rps²  = 1 rad/s² 
• 1rps²  =  2/π rad/s² 

Solution

Both, rad/s ²  and rps ²   are units of angular acceleration.1 rps ²  =  2π rad/s ²  

Q11. A body is moving with constant velocity parallel to x axis. Its angular momentum w.r.t origin will

• remains constant
• increases
• decreases
• become zero

Solution

Angular momentum L = r × p L = mv (rsinθ) Neither p (mv) nor perpendicular distance from x axis(r sinθ) changes hence angular momentum(L) with respect to origin remains constant.  

Q12. The moment of inertia of a body is independent of

• its mass
• its shape and size
• its angular velocity
• choice of axis of rotation

Solution

The moment of inertia of a body is independent of its angular velocity.It depends upon the position and orientation of the axis of rotation,shape and size of the body and distribution of mass of the body about the axis of rotation.

Q13. A boy is playing with a tire of radius 0.5m. He accelerates it from 5rpm to 25 rpm in 15 seconds. The linear acceleration of tire is

• 7 m/s²
• 10 m/s²
• 70 m/s²
• 0.07 m/s²

Solution

Q14. Which of the following doesn't use the application of Conservation of Angular Momentum?

• A skater performing a fast spin
• A diver performing somersaults while diving
• Cat landing gently on feet
• Fruit falling off the tree

Solution

Fruit falling off the tree doesn't use the concept of Conservation of Angular Momentum rest all use it.

Q15. A pair of equal and opposite forces with different line of action are said to form a 

• moment
• couple
• momentum
• inertia

Solution

The pair of equal and opposite forces with different line of action are said to form a couple.

Q16. The motion of centre of mass of a system of two particles is unaffected by their internal forces

• Irrespective of the actual direction of the internal forces
• only if they are along the line joining the particles
• only if they are at right angles to the line joining the particles
• only if they are obliquely inclined to the line joining the particles

Solution

Because the centre of mass is affected only by external forces not by internal forces.

Q17. A circus acrobat while performing spins brings his limbs closer to the body. Due to this

• Angular Momentum is conserved and also K.E. is conserved.
• Angular Momentum is not conserved and also K.E. is not conserved.
• Angular Momentum is not conserved but K.E. is conserved
• Angular Momentum is conserved but K.E. is not conserved

Solution

A circus acrobat while performing spins brings his limbs closer to the body. Due to this Angular Momentum is conserved but K.E. is not conserved. Because when the moment of inertia decreases, rotational kinetic energy increases as work is done in decreasing the moment of inertia of the body.

Q18. The centre of mass of a body is located

• inside or outside the system
• inside the system
• outside the system
• at the centre of system

Solution

The centre of mass of a body is located inside or outside the system

Q19. A proton and an electron, initially at rest, are allowed to move under their mutal attractive force. Their centre of mass will:

• move towards the proton
• move towards the electron
• remain stationary
• move in an unpredictable manner.

Solution

We require an external force to move the centre of mass of a system of particles. The mutual force of electrical attraction is an internal force which can not affect the position of the centre of mass of the system.

Q20. A man standing on a table rotating about the central axis pulls his hands holding the dumb bells towards chest.  How the angular velocity will change?

• increase
• decrease
• remains same
• increase or decrease depending on the magnitude of angular velocity of the wheel.

Solution

When the man pulls his hands towards chest, the moment of inertia will decrease and due to conservation of angular momentum, angular velocity will increase.

Q21. An iron made, regular shaped body moves with an initial velocity of “v” on an inclined plane. It reaches to a maximum height of 7 v ²/10  g.What is the geometrical shape of the body?

• a sphere
• a ring
• a rod
• a cylinder

Solution

Q22. There are some passengers inside a stationary railway compartment. The centre of masses of the compartment itself(without the passengers) is C1, while the centre of mass of the compartment plus passengers' system is C2. if the passengers moves about inside the compartment

• both C1 and C2 will move with respect to the ground
• neither C1 nor C2 will move with respect to the ground
• C1 will move but C2 will be stationary with respect to the ground.
• C2 will move but C1 will be stationary with respect to the ground.

Solution

Since the compartment (including passenger) is stationary the combined centre of mass of the compartment and passengers is fixed, i.e C ₂ is fixed.When the passengers move here and there in the compartment then in an attempt to keep C ₂ fixed C ₁ has to move.

Q23. The angular momentum of a system of particles is not conserved when

• net external force acts on the system
• net external torque acts on the system
• net external impulse acts on the system
• none of above

Solution

Angular momentum can change only when external torque acts on the system

Q24. A car decelerates uniformly from velocity v₁ to velocity v₂ while getting displaced by s.  If the diameter of the wheel is d, the angular acceleration of the wheel is

• (v₁² - v₂²)/ ds
• (v₂ - v₁) / ds
• (v₁ - v₂) / ds
• (v₂² - v₁²) /ds

Solution

The acceleration 'a' of the car is given by v₂² = v₁² + 2as (we have applied th equation of linear motion,  v² = v₀²+2as) Therefore, a = (v₂² - v₁²) /2s. The angular acceleration of the wheel is given by  =a/r where r is the radius of the wheel (which is equal to d/2). Therefore,

Q25. The moment of momentum is known as

• torque
• angular momentum
• moment of force
• moment of inertia

Solution

The moment of momentum is known as angular momentum.

Q26. A body is rolling down an inclined plane without slipping. How does the acceleration of the rolling body depend on its radius?

• It is directly proportional to the radius
• It is directly proportional to the square root of radius
• It is inversely proportional to the square root of radius
• It does not depend upon radius

Solution

The acceleration of the rolling body is independent of its radius

Q27. Two identical particles move towards each other with velocity 2v and v respectively. The velocity of the centre of mass is

• v
• v/3
• v/2
• zero

Solution

 

Q28. Two rings have their moment of inertia in the ratio 2:1 and their diameters are in the ratio 2:1. The ratio of their masses will be:

• 2:1
• 1:2
• 1:4
• 1:1

Solution

Q29. To maximize torque on a lever, which of the following will not help?

• Increasing the magnitude of the force, F that we apply.
• Increasing the distance, r, from the axis of rotation of the point to which you apply the force
• Increasing the density of material.
• Apply the force in a direction perpendicular to the lever

Solution

To maximize torque, you need to: i. Increase the magnitude of the force ii. Increase the distance, r, from the axis of rotation of the point where we apply the force. iii. Apply the force in a direction perpendicular to the lever.

Q30. The motion of a potter's wheel is an example of

• translatory motion
• rotatory motion
• rolling motion
• precessional motion

Solution

The motion of a potter's wheel is an example of rotatory motion

Q31. Which of the following is not an example of couple?

• Compass needle in the earth's magnetic field
• Opening the lid of a bottle by turning its finger
• Balancing a see-saw
• Increase in the angular velocity of a planet when it comes nearer to the sun.

Solution

Increase in the angular velocity of a planet when it comes nearer to the sun is an example of law of conservation of angular momentum.

Q32. All the points of a rigid body rotating about the given axis have same :   

• Linear velocity
• Angular velocity
• Linear acceleration
• Angular momentum

Solution

All the points of a rigid body rotating about the given axis have same angular velocity.

Q33. The sum of moments of masses of all the particles in a system about the centre of mass is always:

• maximum
• minimum
• infinite
• zero

Solution

The sum of moments of masses of all the particles in a system about the centre of mass is always zero.

Q34. The centre of mass of a system of particles does not depend on

• forces on the particles.
• position of the particles.
• masses of the particles
• relative distances between the particles.

Solution

The centre of mass of a system of particles does not depend on forces on the particles.

Q35. If the resultant of all external forces is zero, then velocity of centre of mass will be

• zero
• constant
• maximum
• minimum

Solution

If the resultant of all external forces is zero, then velocity of centre of mass will be constant.             

Q36. There are two circular iron discs A and B having masses in the ratio 1:2 and diameter in the ratio 2:1. The ratio of their moment of inertia is

• 2:1
• 1:3
• 4:1
• 8:1

Solution

  

Q37. Four billiards balls, each of mass 0.5 kg, all are travelling in the same direction on a billiard table, with speeds of 2 m/s, 4 m/s, 8 m/s and 10 m/s.  What is the linear momentum of this system?

• 10 kg-m/s
• 2 kg-m/s
• 5 kg-m/s
• 12 kg-m/s

Solution

The linear momentum of a system is simply the sum of the linear momentum of the constituent parts.  Thus we only need to find the momentum of each ball : P = m₁v₁ + m₂v₂ + m₃v₃ + m₄v₄ = 1+2+4+5 = 12 Thus the total momentum of the system is 12 kg-m/s.

Q38. The SI unit of centre of mass is

• m
• kg m
• kg m²
• kg

Solution

The SI unit of centre of mass is m.

Q39. Moment of inertia of a solid sphere of mass M and radius R is ______

• 2/5MR²
• MR²
• 1/2MR²
• 2/3 MR²

Solution

Moment of inertia of a solid sphere of mass M and radius R is (2/5)MR²

Q40. The dimensional formula for the torque is

• [M¹L¹T^-2]
• [M¹L²T^-2]
• [M¹L²T^-1]
• [M¹L¹T^-1]