Daily Practice Problems System of Particles and Rotational Motion

Question 1:

A solid disc of mass M and radius R rolls without slipping down an inclined plane of height h and angle of inclination θ. What is the linear acceleration of the disc? [Level: Hard]

(a) 2g sin θ

(b) g cos θ

(d) g cos

Question 2:

Assertion: The moment of inertia of a solid sphere is greater than that of a hollow sphere with the same mass and radius.

Reason: The moment of inertia depends on the mass distribution and distance from the axis of rotation, and in a solid sphere, the mass is distributed farther from the axis compared to a hollow sphere.

[Level: Moderate]

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(d) A is false but R is true.

Question 3:

The moment of inertia of a body about a given axis is 2.5 kgm. × Initially, the body is at rest. In order to produce a rotational KE of 1000 joule, an angular acceleration of 35 rad/sec must be applied about that axis for a duration of [Level: Easy]

(a) 7.5 s

(b) 0.81 s

(c)

(d) 0.65 s

Question 4:

What is the location of the center of mass for a circular plate with a diameter of 50 cm, after removing a circular section with a diameter of 40 cm from one edge? [Level: Moderate]

(a) 7.3 cm

(b) 5 cm

(d) 7 c

Question 5:

A square frame is created by four identical, thin rods, each of mass M and length l. What is this frame's moment of inertia about an axis that passes through the centre of the square and is parallel to its plane? [Level: Moderate]

(a) ML²

(b) ML²

(d) ML²

Question 6:

The radius of gyration about the centroidal axis perpendicular to the plane increases by a factor of two if a disc of mass 'm' and radius 'r' is reshaped into a ring of radius '3r'. [Level: Moderate]

(a) 2

(b) 2

(d) 4

Question 7:

Two bodies of mass 2 kg and 5 kg have position vectors and

, respectively. What is the position vector of the center of mass of this system. [Level: Easy]

(a)

(b)

(c)

(d)

Question 8:

The ratio of the gyrating radii of a circular ring and a disc with the same mass and radius around each object's axis is: [Level: Easy]

(a) 2 : 1

(b) 2 : 3

(d) 1 : 2

Question 9:

A wheel has angular acceleration of 5.0 rad/s² and an initial angular speed of 2.5 rad/s. In a time of 3s it has rotated through an angle of: [Level: Moderate]

(a) 4

(b) 12

(d) 6

Question 10:

A child sits stationary at one end of a long trolley moving uniformly with a speed 𝑉 on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system? [Level: Moderate]

Question 11:

A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 50 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 1/5 times the initial value? Assume that the turntable rotates without friction. [Level: easy]

Question 12:

The centre of gravity of a 3 m long rod will be at and its mass acting per unit length will be directly proportional to the distance x from one of its ends. [Level: Moderate]

Question 13:

A rope of negligible mass is wound round a hollow cylinder of mass 5 kg and radius 30 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 40 N? What is the linear acceleration of the rope? Assume that there is no slipping. [Level: Moderate]

Question 14:

How far does the wheel's centre move during a single rotation? If the wheel's radius is R. [Level: Easy]

(a) R

(b) πR

(d) 0

Question 15:

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 7 g are put one on top of the other at the 15 cm mark, the stick is found to be balanced at 40.0 cm. What is the mass of the metre stick?

[Level: Moderate]

Question 16:

A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision.

[Level: Hard]

Question 17:

A ring and a disc with equal radii and masses arranged in a 3:2 ratio are made to revolve around their central axis. When they are both at rest, the same torque acts upon them. When torque is released from both at once, which one will have a greater angular velocity? [Level: Hard]

(a) Ring

(b) Disc

(d) Depends on ratio of mass and radius

Question 18:

A and B are two circular discs with equal masses and thicknesses but different densities of metal (dA > dB). If their moments of inertia are Ia and Ib about an axis that is normal to the circular faces and passes through the centre, then [Level: Hard]

(a) I_a = I_b

(b) I_a > I_b

(d) None of these

Question 19:

A pulley of radius 0.2 m and moment of inertia 0.05 kg·m² is connected to a mass of 2 kg via a light string. If the mass is allowed to fall vertically, what is the angular acceleration of the pulley as the mass descends? [Level: Moderate]

Question 20:

What percentage must K.E increase if an object's rotational velocity is increased by 50%? [Level: Easy]

(a) 40 %

(b) 20 %

(d) 21 %

**********

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All About Daily Practice Problems on NEET Physics System of Particles and Rotational Motion NCERT Chapter 7

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on NEET Physics System of Particles and Rotational Motion NCERT Chapter 7 useful.

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