Browse and search thousands of solved questions for your preparation.
Free questions with full explanations — locked behind signup to protect quality.
A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first $2\text{ s}$, it rotates through an angle $\theta_1$. In the next $2\text{ s}$, it rotates through an additional angle $\theta_2$. The ratio of $\frac{\theta_2}{\theta_1}$ is:
Find the torque about the origin when a force of $3\hat{j} \text{ N}$ acts on a particle whose position vector is $2\hat{k} \text{ m}$.
If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then:
Tritium, a radioactive isotope of hydrogen, emits which of the following particles?
A block of mass 4 kg is suspended through two light spring balances A and B connected in series. Then A and B will read respectively:
Cell in $G_0$ phase :
A round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its center is placed over another disc of moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is:
The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in the time interval from zero to 8 seconds will be:
The average kinetic energy of a gas molecule can be determined by knowing:
A body of mass $m$ is kept on a rough horizontal surface (coefficient of friction = $\mu$). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\vec{F}$, where:
The dimensional formula for Planck's constant (h) is
From a circular ring of mass $M$ and radius $R$, an arc corresponding to a $90^\circ$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $K$ times $MR^2$. The value of $K$ will be:
The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)
When two surfaces are coated with a lubricant, then they:
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is:
A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice. The value of $h$ is: [Latent heat of ice is $3.4 \times 10^5 \text{ J/kg}$ and $g = 10 \text{ N/kg}$]
Two rods, $A$ and $B$, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:
Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of kinetic friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is (g = 10 m/s²):
A block of mass $M=5 \text{ kg}$ is resting on a rough horizontal surface for which the coefficient of friction is 0.2. When a force $F=40 \text{ N}$ is applied, the acceleration of the block will be: ($g=10 \text{ m/s}^2$)
A stone is thrown with an initial speed of $4.9 \text{ m/s}$ from a bridge in vertically upward direction. It falls down in water after $2 \text{ sec}$. The height of the bridge is: