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A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?
Two particles of mass $5 \text{ kg}$ and $10 \text{ kg}$ respectively are attached to the two ends of a rigid rod of length $1 \text{ m}$ with negligible mass. The centre of mass of the system from the $5 \text{ kg}$ particle is nearly at a distance of:
In an orbital motion, the angular momentum vector is:
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $D_1$ has $2\text{ kg}$ mass and $0.2\text{ m}$ radius and initial angular velocity of $50\text{ rad s}^{-1}$. Disc $D_2$ has $4\text{ kg}$ mass, $0.1\text{ m}$ radius and initial angular velocity of $200\text{ rad s}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in $\text{rad s}^{-1}$) of the system is
Ratio of total kinetic energy and rotational kinetic energy in the motion of a disc is:
Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with moments of inertia $I_A$ and $I_B$ ($I_B > I_A$) have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then:
A uniform rod AB of length $l$ and mass $m$ is free to rotate about point A. The rod is released from rest in horizontal position. Given that the moment of inertia of the rod about A is $\frac{ml^2}{3}$, the initial angular acceleration of the rod will be:
Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?
A light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is:
In uniform circular motion:
If rotational kinetic energy is $50\%$ of translational kinetic energy, then the body is:
The increase in the width of the depletion region in a p-n junction diode is due to :
An automobile moves on a road with a speed of $54 \text{ km h}^{-1}$. The radius of its wheels is $0.45 \text{ m}$ and the moment of inertia of the wheel about its axis of rotation is $3 \text{ kg m}^2$. If the vehicle is brought to rest in $15 \text{ s}$, the magnitude of average torque transmitted by its brakes to the wheel is:
Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momenta, then the ratio $p_1 : p_2$ is equal to:
A solid cylinder of mass $50 \text{ kg}$ and radius $0.5 \text{ m}$ is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2 \text{ rev/s}^2$ is:
Two bodies with kinetic energies in the ratio of $4 : 1$ are moving with equal linear momentum. The ratio of their masses is:
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
A rope is wound around a hollow cylinder of mass $3\text{ kg}$ and radius $40\text{ cm}$. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $30\text{ N}$?
Three masses are placed on the x-axis: $300 \text{ g}$ at the origin, $500 \text{ g}$ at $x = 40 \text{ cm}$, and $400 \text{ g}$ at $x = 70 \text{ cm}$. The distance of the center of mass from the origin is:
A man of $50 \text{ kg}$ mass is standing in a gravity free space at a height of $10 \text{ m}$ above the floor. He throws a stone of $0.5 \text{ kg}$ mass downwards with a speed $2 \text{ m s}^{-1}$. When the stone reaches the floor, the distance of the man above the floor will be: