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A rod of length $L$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased then the stress force developed in it is proportional to

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Magnetic dipole moment of a uniformly charged square plate of side $l$ and charge $Q$ rotating about an axis passing through center of mass and perpendicular to plane with angular velocity $\omega$ is

For given conducting shells equivalent capacitance between A & B is

An uniformly charged thin ring has radius $10\text{cm}$ and total charge $12\text{nC}$. An electron is placed on the ring's axis at a distance $25\text{cm}$ from the centre of the ring and is constrained to stay on the axis of ring. The electron is then released from rest. Find the speed of electron when it reaches the center of the ring.

A car of mass $1000\text{kg}$ negotiates a banked curve of radius $90\text{m}$ on a frictionless road. If the banking angle is ${45}^{\circ }$, the speed of the car is:

Take $g=10{\text{m/s}}^2$

The bob of a simple pendulum (mass m and length l) dropped from a horizontal position strikes a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be

The figure below shows a uniform rod of length $30\text{cm}$ having a mass of $3.0\text{kg}.$ The strings as shown in the figure are pulled by constant forces of $20\text{N}$ and $32\text{N}$. Find the force exerted by the $20\text{cm}$ part of the rod on the $10\text{cm}$ part. All the surfaces are smooth, and the strings are light.

A small metal bearing of mass $m_1=30\text{g}$, moving with a velocity of $v_1=25\text{m/s}$ collides elastically with a huge sphere of mass $200\text{kg}$ moving with a velocity of $3\text{m/s}$. What is the velocity of the small metal bearing after colliision?

The $20\text{cm}$ diameter disc in the figure can rotate on the axle through its center. What is the net torque about $\text{O}$ (in $\text{Nm}$)?

X-rays of wavelength $10\mathring{\text{A}}$ is incident on a crystal plane at an angle of ${60}^{\circ }$ from the normal. What should be the distance between the planes, so that the X-rays undergo constructive interference of second order?

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Q49. ‘India Quake’ and ‘Sagar Vani’ app have been launched by Ministry of:

When the angle of incidence is ${60}^{\circ }$ on the surface of a glass slab, it is found that the reflected ray is completely polarized. The velocity of light in glass is,

Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium?

Three identical rods of same material are joined to form an equilateral triangle. The temperature of end A and b is maintained constant as $\sqrt{3}T$ and $T$. The ratio of T_C/T_B will be (Assuming no loss of heat from surfaces)

From the circular disc of radius $4R$, two small discs of radius $R$ are cut off. The centre of mass of the new structure will be at

A
large steel wheel is to be fitted on to a shaft of the same material.
At 27 °C, the outer diameter of the shaft is 8.70 cm and the
diameter of the central hole in the wheel is 8.69 cm. The shaft is
cooled using ‘dry ice’. At what temperature of the shaft
does the wheel slip on the shaft? Assume coefficient of linear
expansion of the steel to be constant over the required temperature
range: α_steel
= 1.20 × 10^–5
K^–1.

How many electrons are there in 1 coulomb of charge?

Two bodies A and B are at positions (2, 3) m and (5, 7) m respectively. These two are moving with constant velocity $3m{s}^{-1}$ along –ve y axis and $4m{s}^{-1}$ along +ve x axis respectively. Minimum separation between them during their motion is

A particle is initially at rest, moves along in a circle of radius $R=2\text{m}$ with an angular acceleration $\alpha =\frac{\pi }{8}{\text{rad/sec}}^2$. The magnitude of average velocity of the particle over the time it moves by half of the circle is

Find the height over the earth's surface at which the weight of a body becomes half of its value at the surface.