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A conductor of length $l$ and mass $m$ carrying $i$ is placed on a smooth incline plane making an angle $\theta$ with horizontal. A magnetic field $B$ is directed vertically upwards. Then for equilibrium of the conductor $\cot \theta$ is given by

How to calculate the dimensional formula for gravitational constant

A metal wheel with $8$ metallic spokes, each $40\text{cm}$ long, is rotated at a speed of $120\text{rev/min}$ in a plane perpendicular to earth's magnetic field of $0.3\times {10}^{-4}\text{T}.$ Find the magnitude of the induced emf between the axis and the rim of the wheel (approximately).

A system consists of block A and B of same mass $5kg$ and connected to the pulley as shown in figure. Find the minimum relative acceleration with which they will move?
(Take $g=10m/s^2$)

A small block of mass $m$ rests on a smooth wedge of angle $\theta$. With what horizontal acceleration $a$ should the wedge be pulled, as shown in the figure, so that the block falls freely.

A transverse pulse generated at the bottom of the uniform vertical rope of length $L$ travels in upward direction. The time taken by the pulse to reach the top of the rope will be :

Find the emf and internal resistance of a single battery which is equivalent to a combination of three batteries as shown in the figure.

A smooth block is released from rest on an incline plane of inclination $\theta$ and length $l$. The time taken to slide down the rough incline is $\alpha$ times the time taken to slide down the smooth incline. The coefficient of friction is

A particle is moving in a circular path with an angular velocity of $2\text{rad/s}$ and angular acceleration of $\alpha =\frac{5}{2}\omega$, where $\omega$ is the angular velocity at any particular instant. Find the angular velocity after the particle has moved through an angle of $3\pi$.

A rifle shoots a bullet from the ground level with a muzzle velocity of $400\text{m/s}$ at a small target $400\text{m}$ away on the ground. The height above the target at which the bullet must be aimed to hit the target is $(g=10{\text{ms}}^{-2})$

A ball falls on an inclined plane of inclination $\theta ={30}^{\circ }$ from a height $h=10\text{m}$ above the point of impact and makes a perfectly elastic collision. Find the distance where will it hit the plane again from the initial point of impact. $(\text{Take}g=10{\text{m/s}}^2)$

A charged particle enters a uniform magnetic field with velocity vector at an angle of 45⁰ with the magnetic field. The pitch of the helical path followed by the particle is p. The radius of the helix will be

There is a chain of length $6\text{m}$ and coefficient of friction $\frac{1}{2}$. What will be the maximum length of chain which can be held outside the table without sliding?

If
the solenoid in Exercise 5.5 is free to turn about the vertical
direction and a uniform horizontal magnetic field of 0.25 T is
applied, what is the magnitude of torque on the solenoid when its
axis makes an angle of 30° with the direction of applied field?

Several capacitors are connected as shown in the given figure. If the charge on the $5\mu \text{F}$ capacitor is $120\mu \text{C}$ , the potential between points $A$ and $D$ is

A particle starts from $x=0$ and moves along a straight line such that its velocity $v$ depends on position $x$ as $v=x+4$.
For the first four seconds, average speed of the particle (in $m/s$) is

A neutron having KE 5eV is incident on a
hydrogen atom in its ground state. The collision-

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26\times {10}^3$ seconds to complete a revolution while its centripetal acceleration is $9.92m/s^2$ . Height of satellite above surface of earth is (Radius of earth $6.37\times {10}^6$ m)

Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

A charge $Q$ is divided into two parts $q$ and $Q-q$. Find the relationship between $Q$ and $q$ , if the two parts placed at a given distance $r$ apart have the maximum coulomb repulsion force?

If the critical angle for the total internal reflection from a medium to vacuum is $30°$. The velocity of light in the medium is

Point $A$ of rod $AB$ $(l=2\text{m})$ is moving upwards against a wall with velocity $v=2\text{m/s}$. Find angular speed of the rod at an instant when $\theta ={60}^{\circ }$

A triangular wire frame, each side of $2m$ is placed in a region of time variant magnetic field having $\frac{dB}{dt}=\sqrt{3}T/s$ . The magnetic field is perpendicular to the plane of the triangle. The base of the triangle $AB$ has a resistance $1\Omega$ while the other two sides have resistance $2\Omega$ each. The magnitude of the potential difference between the points $A$ and $B$ will be

(Note: Magnetic field is absent inside the triangular loop)

Two identical coherent sources placed on a diameter of a circle of radius $R$ at separation $x(<<R)$ symmetrically about the center of the circle. The sources emit identical wavelength $\lambda$ each. The number of points on the circle with maximum intensity is $(x=5\lambda )$ :

For the electric field shown in figure, its vector representation will be