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In the circuit shown in the figure, a meter bridge is in its balance state. The meter bridge wire has a resistance of $0.1$$\Omega$/$\text{cm}$. Calculate the value of unknown resistance $X$ and the current drawn from the battery of negligible internal resistance.

What is the lengt of side b?

The force $\left(F\right)$ that needs to be applied on water in the thicker arm so that the water may remain in equilibrum is

For the situation shown in the figure, if the spring is elongated by ${}^{\prime }{x}^{\prime }$. The condition for no slipping on the inclined plane is given by

Surface mass density of a semicircular disk varies with position as $\sigma ={\sigma }_0\frac{r}{R}$ where ${\sigma }_0$ is constant, $R$ is the radius of the disc and $r$ is measured from the centre of the disc. Find the COM of the disc.

The speed of a boat in still water is $\sqrt{5}\text{m/s}$ . While crossing a river, the average speed of the boat is $3\text{m/s}$. If boat crosses the river in the shortest possible time, what is the speed of flow of water?

If the uncertainty in position and momentum are equal, then the uncertainty in velocity is:

The moment of inertia of the plate of mass $M$ about $x-$ axis is

Electrostatic field is zero the conductor.

For given combination of capacitor where each capacitance is C

Potential of terminal P is

Figure shows the roller coaster track. Each car will start from rest at point $A$ and roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is $(g=10m/s^2)$

Find the wavelength of electron in the 2nd orbit of $H{e}^{+}$ ion

A motorcycle is moving with speed $20\text{m/s}$ on the road. The M.O.I of wheel about its axis of rotation is $2{\text{kg m}}^2$ and radius of its wheel is $0.5\text{m}$. Motorcycle comes to rest in $10\text{sec}$ after applying the breaks. Find the magnitude of the average torque transmitted by its brakes to the wheel?

If the speed of the wave shown in the figure is 330 m/s in the given medium, then the equation of the wave propagating in the positive x - direction will be -(all quantities are in MKS units)

A semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in figure. The distance of centre of mass $\text{C}$ of remaining plate, from point $\text{O}$ is

Two flasks of equal volume connected by a narrow tube (of negligible volume) are at ${27}^{\circ }C$ and contain 0.70 mole of $H_2$ at 0.5 atm. One of the flasks is then immersed into a hot bath, kept at ${127}^{\circ }C$, while the other remains at ${27}^{\circ }C$. Calculate the final pressure.

An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol^–1 K^–1, molecular mass of O₂ = 32 u).

Which of the following remains unchanged when the sound wave travels from air to water?

In Young's double slit experiment the phase difference between the waves reaching the central fringe and fourth dark fringe will be

A charged particle having mass $\left(m\right)$ and charge $\left(q\right)$ is projected from the origin with velocity $v=v_0\hat{i}$ in a uniform magnetic field, $B=\frac{B_0}{2}\hat{i}+\frac{\sqrt{3}{B}_0}{2}\hat{j}$ pitch of the helical path described by the particle is ?

In making an alloy, a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$; then the specific gravity of the alloy is

Three equal negative charges, $-q_1$ each, form the vertices of an equilateral triangle. A particle of mass $m$ and a positive charge $q_2$ is constrained to move along a line perpendicular to the plane of triangle and through its centre which is at a distance $r$ from each of the negative charges as shown in the figure. The whole system is kept in gravity free space. Find the time period of vibration of the particle for small displacement from equilibrium position.

A particle is projected from the bottom of an inclined plane of angle ${30}^{\circ }$ with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ with the horizontal. Find the time of flight.

(Take $g=10m/s^2$)