OnlineCBT
Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Practice questions & answers
Find a question, read its answer and explanation, then practise related questions.
Physics SYSTEMS OF PARTICLES AND ROTATIONAL MOTION · Clear filters
193 questions
Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A force \( \mathbf{F} = (2\hat{i} - 5\hat{j} + 3\hat{k})\text{ N} \) acts at a point \( P(1, -2, 3)\text{ m} \). The torque of this force about the reference point \( A(2, 0, -1)\text{ m} \) is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
An engine transmits a constant power of 15 kW to a shaft rotating at a steady angular speed of 300 rpm. The torque delivered by the engine to the shaft is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A uniform metre stick is balanced on a knife edge at its centre (\( 50.0 \text{ cm} \) mark). When two identical coins, each of mass \( 5.0 \text{ g} \), are placed one on top of the other at the \( 12.0 \text{ cm} \) mark, the stick is found to be balanced about the knife edge at the \( 45.0 \text{ cm} \) mark. The mass of the metre stick is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A motor wheel begins to rotate from rest with a uniform angular acceleration \( \alpha \). If it completes \( n_1 \) revolutions in the first \( t \) seconds and an additional \( n_2 \) revolutions in the next \( t \) seconds, then the ratio \( n_2 / n_1 \) is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A non-uniform thin rod of length \( L \) lies along the \( x \)-axis with one end at the origin \( x = 0 \). Its linear mass density varies as \( \lambda(x) = \lambda_0 (1 + \frac{x}{L}) \), where \( \lambda_0 \) is a positive constant. The distance of the centre of mass of the rod from the origin is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A force \( \mathbf{F} = (a\hat{i} + 3\hat{j} + 6\hat{k})\,\text{N} \) is acting at a point whose position vector is \( \mathbf{r} = (2\hat{i} - 6\hat{j} - 12\hat{k})\,\text{m} \). The value of \( a \) for which angular momentum about the origin is conserved is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Consider the following statements regarding the vector product (cross product) of two vectors \( \mathbf{a} \) and \( \mathbf{b} \): (A) \( \mathbf{a} \times \mathbf{b} = -\mathbf{b} \times \mathbf{a} \) (B) \( \mathbf{a} \times (\mathbf{b} + \mathbf{c}) = \mathbf{a} \times \mathbf{b} + \mathbf{a} \times \mathbf{c} \) (C) \( \mathbf{a} \times \mathbf{a} = 0 \) (D) Under coordinate reflection, \( \mathbf{a} \times \mathbf{b} \) reverses its direction. Which of the above statements are correct?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Given below are two statements regarding rotation about a fixed axis: Statement I: The particles situated directly on the fixed axis of rotation remain stationary. Statement II: The linear speed of any particle of the rigid body is directly proportional to its perpendicular distance from the axis of rotation. In the light of the above statements, choose the most appropriate answer from the options given below:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A couple consists of two forces \( \mathbf{F}_1 = (2\hat{i} + 3\hat{j} - \hat{k})\text{ N} \) acting at point \( A(1, -1, 2)\text{ m} \) and \( \mathbf{F}_2 = (-2\hat{i} - 3\hat{j} + \hat{k})\text{ N} \) acting at point \( B(3, 2, -1)\text{ m} \). The magnitude of the moment of this couple is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Two forces of equal magnitude \( F = 25\,\text{N} \) act in opposite directions along parallel lines separated by a perpendicular distance of \( 0.8\,\text{m} \), forming a couple. If the origin is chosen at a point \( 0.5\,\text{m} \) outside the region between the forces along the common normal line, the net torque of this couple about this origin is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
The angular speed of a flywheel increases uniformly from \( 1200\text{ rpm} \) to \( 3120\text{ rpm} \) in \( 16\text{ seconds} \). The angular acceleration of the flywheel is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A solid cylinder is rolling down an inclined plane without slipping. At any given instant, the velocity of the point of contact of the cylinder with the plane is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Refer to the given figure depicting a cylinder rolling without slipping down an inclined plane. At the instant shown, if the centre of mass of the cylinder \( P_1 \) is moving with a speed \( v \), what are the magnitudes of the instantaneous velocities of the contact point \( P_3 \) and the uppermost point \( P_4 \)?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
In the mechanical setup shown below, a non-uniform bar of weight \( W \) and length \( 2 \text{ m} \) hangs horizontally in static equilibrium supported by two light strings. The strings make angles \( 36.9^\circ \) and \( 53.1^\circ \) with the vertical walls. The ratio of the tensions in the left string to the right string (\( T_1 / T_2 \)) is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A rigid body rotates about a fixed axis. If its angular velocity changes with time according to \( \omega(t) = 3t^2 + 4t + 2\text{ rad/s} \), the angular acceleration of the body at \( t = 2\text{ s} \) is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Under a parity inversion transformation (reflection through the origin: \( x \to -x, y \to -y, z \to -z \)), how do the polar vector \( \vec{r} \) and the axial vector \( \vec{\tau} = \vec{r} \times \vec{F} \) transform respectively?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Which of the following conditions is both necessary and sufficient for the centre of mass of a continuous body to coincide with its geometric centre?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
For a rigid body rotating about a fixed \( z \)-axis, why do internal forces between particles do zero net work during rotation?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Consider the following statements regarding rotational motion of a rigid body about a fixed axis: (A) The angular velocity vector \( \boldsymbol{\omega} \) lies along the fixed axis of rotation. (B) The linear velocity \( \mathbf{v} \) of any particle is given by \( \mathbf{v} = \mathbf{r} \times \boldsymbol{\omega} \). (C) For a fixed axis, the angular acceleration \( \boldsymbol{\alpha} \) also lies along the axis of rotation. (D) A force whose line of action intersects the axis of rotation produces maximum torque. Which of the above statements are correct?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Consider the following statements regarding the motion of the centre of mass of an isolated system of particles: (A) The internal forces between particles always cancel in pairs due to Newton's third law and cannot alter the total linear momentum of the system. (B) If the net external force on the system is zero, the centre of mass must permanently remain at rest. (C) A projectile exploding mid-air continues to have its centre of mass follow the same parabolic path until any fragment hits the ground. (D) For an unstable nucleus decaying at rest, the fragments fly apart such that the total linear momentum in the centre-of-mass frame is always zero. Which of the above statements are correct?
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
The radius of gyration of a uniform thin rod of length \( L \) about an axis perpendicular to the rod and passing through its midpoint is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
A non-uniform thin rod of length \( L \) has linear mass density given by \( \lambda(x) = k x^2 \), where \( x \) is measured from its left end and \( k \) is a constant. The position of its centre of mass from the left end is:
Read answer →Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
