11th Physics Monthly Test - 1 ( Motion of System of Particles and Rigid Bodies )

MABS Institution

11th Physics Monthly Test - 1 ( Motion of System of Particles and Rigid Bodies )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

When a child sits stationary at one end of a long trolley moving uniformly with some speed on a smooth horizontal plane. The speed of the centre of mass of the system (child and trolley):

increases
decreases
remains same
changes

A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions) The directions of the frictional force acting on the cylinder are:

up the incline, while ascending and down the incline, while descending
up the incline, while ascending as well as descending
down the incline, while ascending and up the incline, while descending
down the incline, while ascending as well as descending

For a hollow cylinder and a solid cylinder rolling without slipping on a inclined plane, then which of these reaches earlier:

solid cylinder
hollow cylinder
both simultaneously
can't say anything

While negotiating a circular level road a cyclist has to bend by an angle θ from vertical to stay in an equilibrium is

\(tan \theta=\frac{rg}{r^{2}}\)
\(\theta=tan^{-1} (\frac{v^{2}}{rg})\)
\(\theta = sin^{-1}(\frac{rg}{r^{2}})\)
zero

Consider a system of two identical particles. One is at rest and the other has an acceleration \(\overrightarrow { a } \) .The centre of mass has an acceleration

1/2\(\overrightarrow { a } \)
\(\overrightarrow { a } \)
2\(\overrightarrow { a } \)
Zero

Moment of inertia of a thin uniform rod about an axis passing through the center of mass and perpendicular to the length is

\(\frac{1}{3}Ml^{2}\)
\(\frac{1}{12}Ml^{2}\)
\(\frac{1}{2}m(l^{2}+b^{2})\)
ml²

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the center of mass is

30 m/s
20 m/s
10 m/s
5 m/s

For square and rectangular objects center of mass lies at

the point where the diagonals meet
at the corners
on the center surface
any point

If a body moves through a distance greater than 2R in one full rotation, then:

\({V}_{CM}>{R}_{ω}\)
\({V}_{CM}<{R}_{ω}\)
\({V}_{CM}>{R}_{ω}\)
\({V}_{CM}<{R}_{ω}\)

Moment of inertia does not depend upon:

distribution of mass
axis of rotation
point of application of force
none of these

Part - B

Generic 2 - Answer All Question

State the torque about an axis is independent of the origin.

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

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

A force of \((4\hat{i}-3\hat{j}+5\hat{k})\) N is applied at a point whose position vector is \((7\hat{i}+4\hat{j}-2\hat{k})\)m.Find the torque of force about the origin.
Give an example to show that the following statement is false. 'any two forces acting on a body can be combined into single force that would have same effect'.

When an object will have precession? Give one example.

Can a body in translatory motion have angular momentum? Explain.

What is meant by rolling friction?

A rectangle block rests on a horizontal table. A horizontal force is applied on the block at a height h above the table to move the block. Does the line of action of the normal force N exerted by the table on the block depend on h?

Why there are two propellers in a helicopter?

Part - C

Generic 3 - Answer All Question

State principle of moments

What do you mean by Rigid body?

What is radius of gyration?

Two discs of moments of inertia I₁ and I₂ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed \(\omega_1\) and \(\omega_2\) are brought into contact face to face with their axes of rotation coincident, (i) What is the angular speed of the two-disc system? (ii) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take \(\omega_1 \ne \omega_2\).
A solid sphere is rolling on a frictionless plane surface about its axis of symmetry. Find ratio of its rotational energy to its total energy.

An internal force cannot change the state of motion of centre of mass of a body. How does the internal force of the brakes bring a vehicle to rest?

What are the rotational equivalents for the physical quantities,
(i) mass and
(ii) force?

Calculate the moment of inertia of a cylinder of length 1.5m, radius 0.05m and density 8 X 10³ kg m^-3 about the axis of the cylinder.

If earth contracts to half of its present radius what would be the length of the day at equator?

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 Nm. What is the power required by the engine? Assume that the engine is 100% efficient.

Part - D

Generic 5 - Answer All Question

A man of mass 50 kg is standing at one end of a boat of mass 300 kg floating on still water. He walks towards the other end of the boat with a constant velocity of 2 m s^-1 with respect to a stationary observer on land. What will be the velocity of the boat, (a) with respect to the stationary observer on land? (b) with respect to the man walking in the boat?

[Given: There is friction between the man and the boat and no friction between the boat and water].

Explain the principle of moments of rotational equilibrium? Hence define mechanical advantage?

A hoop of radius 2m weights 100 kg. It rolls along a horizontal floor so that its centre of mass has speed of 20 cm/s. How much work has to be done to stop it?

A constant couple of 500 Nm turns a wheel of moment of inertia 100 kgm²about an axis through its centre. What will be the angular velocity gained by the body after 2 seconds?

Consider a thin uniform circular ring rolling down in an inclined plane without slipping. Compute the linear acceleration along the inclined plane if the angle of inclination is \(45 ^{0}\).
Write an expression for the KE of a body rolling without slipping with centre of mass as reference.

A disc of mass 500 g and radius 10 em can freely rotate about a fixed axis as shown in figure. light and inextensible string is wound several turns around it and 100 g body is suspended at its free end. Find the acceleration of this mass. [Given: The string makes the disc to rotate and does not slip over it. g = 10m s^-2]

Derive an expression for the position vector of the center of mass of particle system.

Three particles of masses m₁= 1 kg, m₂ = 2 kg and m₃ = 3 kg are placed at the comers of an equilateral triangle of side 1m as shown in Figure. Find the position of center of mass.

State and prove perpendicular axis theorem.

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11th Physics Monthly Test - 1 ( Motion of System of Particles and Rigid Bodies )

MABS Institution

11th Physics Monthly Test - 1 ( Motion of System of Particles and Rigid Bodies )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

When a child sits stationary at one end of a long trolley moving uniformly with some speed on a smooth horizontal plane. The speed of the centre of mass of the system (child and trolley):

A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions) The directions of the frictional force acting on the cylinder are:

For a hollow cylinder and a solid cylinder rolling without slipping on a inclined plane, then which of these reaches earlier:

While negotiating a circular level road a cyclist has to bend by an angle θ from vertical to stay in an equilibrium is

Consider a system of two identical particles. One is at rest and the other has an acceleration \(\overrightarrow { a } \) .The centre of mass has an acceleration

Moment of inertia of a thin uniform rod about an axis passing through the center of mass and perpendicular to the length is

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the center of mass is

For square and rectangular objects center of mass lies at

If a body moves through a distance greater than 2R in one full rotation, then:

Moment of inertia does not depend upon:

Part - B

Generic 2 - Answer All Question

State the torque about an axis is independent of the origin.

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

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-1. The radius of the cylinder is 0.25m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

A force of \((4\hat{i}-3\hat{j}+5\hat{k})\) N is applied at a point whose position vector is \((7\hat{i}+4\hat{j}-2\hat{k})\)m.Find the torque of force about the origin.

Give an example to show that the following statement is false. 'any two forces acting on a body can be combined into single force that would have same effect'.

When an object will have precession? Give one example.

Can a body in translatory motion have angular momentum? Explain.

What is meant by rolling friction?

A rectangle block rests on a horizontal table. A horizontal force is applied on the block at a height h above the table to move the block. Does the line of action of the normal force N exerted by the table on the block depend on h?

Why there are two propellers in a helicopter?

Part - C

Generic 3 - Answer All Question

State principle of moments

What do you mean by Rigid body?

What is radius of gyration?

A solid sphere is rolling on a frictionless plane surface about its axis of symmetry. Find ratio of its rotational energy to its total energy.

An internal force cannot change the state of motion of centre of mass of a body. How does the internal force of the brakes bring a vehicle to rest?

What are the rotational equivalents for the physical quantities, (i) mass and (ii) force?

Calculate the moment of inertia of a cylinder of length 1.5m, radius 0.05m and density 8 X 103 kg m-3 about the axis of the cylinder.

If earth contracts to half of its present radius what would be the length of the day at equator?

To maintain a rotor at a uniform angular speed of 200 rad s-1, an engine needs to transmit a torque of 180 Nm. What is the power required by the engine? Assume that the engine is 100% efficient.

Part - D

Generic 5 - Answer All Question

Explain the principle of moments of rotational equilibrium? Hence define mechanical advantage?

A hoop of radius 2m weights 100 kg. It rolls along a horizontal floor so that its centre of mass has speed of 20 cm/s. How much work has to be done to stop it?

A constant couple of 500 Nm turns a wheel of moment of inertia 100 kgm2 about an axis through its centre. What will be the angular velocity gained by the body after 2 seconds?

Consider a thin uniform circular ring rolling down in an inclined plane without slipping. Compute the linear acceleration along the inclined plane if the angle of inclination is \(45 ^{0}\).

Write an expression for the KE of a body rolling without slipping with centre of mass as reference.

Derive an expression for the position vector of the center of mass of particle system.

Three particles of masses m1= 1 kg, m2 = 2 kg and m3 = 3 kg are placed at the comers of an equilateral triangle of side 1m as shown in Figure. Find the position of center of mass.

State and prove perpendicular axis theorem.

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A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

What are the rotational equivalents for the physical quantities,
(i) mass and
(ii) force?

Calculate the moment of inertia of a cylinder of length 1.5m, radius 0.05m and density 8 X 10³ kg m^-3 about the axis of the cylinder.

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 Nm. What is the power required by the engine? Assume that the engine is 100% efficient.

A constant couple of 500 Nm turns a wheel of moment of inertia 100 kgm²about an axis through its centre. What will be the angular velocity gained by the body after 2 seconds?

Three particles of masses m₁= 1 kg, m₂ = 2 kg and m₃ = 3 kg are placed at the comers of an equilateral triangle of side 1m as shown in Figure. Find the position of center of mass.