If the resultant of all external forces acting on a system of particles is zero, then from an inertial frame one can surely say that
  • Linear momentum of the system does not change in time
  • Kinetic energy of the system does not change in time.
  • Angular momentum of the system does not change in time.
  • Potential energy of the system does not change in time.
This question contains Statement – 1 (assertion) and statement – 2 (reason). Of these statements, mark correct choice if Statement 1: If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant. Statement 2: The linear momentum of an isolated system remains constant.
  • Statement - 1 and 2 are true and statement - 2 is a correct explanation of statement - 1
  • Statement -1 and 2 are true and statement - 2 is not a correct explanation of statement - 1
  • Statement – 1 is true and Statement - 2 is false.
  • Statement – 1 is false, statement – 2 is true.
Four-point masses, each of value $m$, are placed at the corners of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is
  • $3ml^2$
  • $ml^2$
  • $2ml^2$
  • $\sqrt3ml^2$
Moment of inertia of a circular wire of mass M and radius R about its diameter is
  • $\frac{1}{2}MR^2$
  • $\frac{1}{4}MR^2$
  • $2MR^2$
  • $MR^2$
Initial angular velocity of a circular disc of mass $M$ is $\omega_1$. Then, two small spheres of mass $m$ are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?
  • $\frac{M+m}{M}\omega_1$
  • $\frac{M}{M+m}\omega_1$
  • $\frac{M}{M+4m}\omega_1$
  • $\frac{M}{M+2m}\omega_1$
A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc. The insect now moves along the diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc,
  • Remains unchanged
  • Continuously decreases
  • Continuously increases
  • First increases and then decreases
The dimensions of angular momentum are
  • $\left[MLT^{-2}\right]$
  • $\left[ML^2T^{-1}\right]$
  • $\left[ML^2T^{-2}\right]$
  • $\left[ML^2T\right]$
The torque $\tau$ on a body about a given point is found to be equal to $\vec{A}\times\vec{L}$, where $\vec{A}$ is a constant vector and $\vec{L}$ is the angular momentum of the body about that point. From this, it follows that
  • $\frac{d\vec{L}}{dt}$ is perpendicular to $\vec{L}$ at all instants of time
  • The component of $\vec{L}$ in the direction of $\vec{A}$ does not change with time
  • The magnitude $\vec{L}$ does not change with time.
  • all the above
A solid sphere of radius $r$ is rolling with velocity $v$ on a smooth plane. The total Kinetic energy of the sphere is
  • $\frac{7}{10}mv^2$
  • $\frac{3}{4}mv^2$
  • $\frac{1}{2}mv^2$
  • $\frac{1}{4}mv^2$
A coin of mass 4.8 Kg and radius one meter is rolling on a horizontal surface without sliding with angular velocity 600 rotations/min. What is total Kinetic energy of the coin?
  • $360 J$
  • $1400\pi^2J$
  • $4000\pi^2J$
  • $600\pi^2J$
Two spheres of masses $M$ and $2M$ are initially at rest at a distance $R$ apart. Due to mutual force of attraction, they approach each other. When they are at separation $R/2$ the acceleration of their center of mass would be
  • $0$
  • $g$
  • $3g$
  • $12g$
In the following question, a statement of assertion is followed by a statement of reason. Mark the correct choice as Assertion: There are very small sporadic changes in the period of rotation of the earth. Reason: Shifting of large masses in the earth’s atmosphere produces a change in the moment of inertia of the earth causing its period of rotation to change.
  • If both assertion ad reason are true and reason is the correct explanation of assertion.
  • If both assertion and reason are true and reason is not correct explanation of assertion.
  • If assertion is true, but reason is false
  • If both assertion and reason are false
In the following question, a statement of assertion is followed by a statement of reason. Mark the correct choice as Assertion: If polar ice melts, days will be longer. Reason: Moment of inertia decreases and thus angular velocity increases.
  • If both assertion ad reason are true and reason is the correct explanation of assertion.
  • If both assertion and reason are true and reason is not correct explanation of assertion.
  • If assertion is true, but reason is false
  • If both assertion and reason are false
In the following question, a statement of assertion is followed by a statement of reason. Mark the correct choice as Assertion: The size and the shape of the rigid body remains unaffected under the effect of external forces. Reason: The distance between two particles remains constant in a rigid body
  • If both assertion ad reason are true and reason is the correct explanation of assertion.
  • If both assertion and reason are true and reason is not correct explanation of assertion.
  • If assertion is true, but reason is false
  • If both assertion and reason are false
In the following question, a statement of assertion is followed by a statement of reason. Mark the correct choice as Assertion: A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion). Reason: For perfect rolling motion, work done against friction is zero
  • If both assertion ad reason are true and reason is the correct explanation of assertion.
  • If both assertion and reason are true and reason is not correct explanation of assertion.
  • If assertion is true, but reason is false
  • If both assertion and reason are false
A disc is rolling and the velocity of its center of mass is. Which one will be correct?
  • The velocity of the highest point is $2v_{cm}$ and the point of contact is zero.
  • The velocity of the highest point is $v_{cm}$ and the point of contact is v_{cm}
  • The velocity of the highest point is ${2v}_{cm}$ and the point of contact is v_{cm}
  • The velocity of the highest point is ${2v}_{cm}$ and the point of contact is ${2v}_{cm}$
Identify the vector quantity among the following
  • distance
  • angular momentum
  • heat
  • energy
Find the torque of the force $\vec{F}=-3\hat{i}+\hat{j}+5\hat{k}N$ acting at the point $\vec{r}=7\hat{i}+3\hat{j}+\hat{k}$
  • $-21\hat{i}+4\hat{j}+4\hat{k}$
  • $-14\hat{i}+34\hat{j}-16\hat{k}$
  • $14\hat{i}-38\hat{j}+16\hat{k}$
  • $4\hat{i}+4\hat{j}+6\hat{k}$
A circular disc is to be made by using iron and aluminum so that it acquired maximum moment of inertia about geometrical axis. It is possible with
  • Aluminum interior and iron surround to it
  • iron interior and aluminum surround to it
  • using iron and aluminum layers in alternate order
  • sheet of iron is used at both external surfaces and aluminum sheet as the internal layer
A ring of mass m and radius r rotates about an axis passing through its center and perpendicular to its plane with angular velocity $\omega$. Its kinetic energy is
  • $\frac{1}{2}mr^2\omega^2$
  • $mr\omega^2$
  • $mr^2\omega^2$
  • $ \frac{1}{2}mr\omega^2$
0 h : 0 m : 1 s

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