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A boy of mass 25 kg stands on a board of mass 10 kg which in turn is kept on a frictionless horizontal surface. The boy makes a jump with a velocity 5 m/s in the horizontal direction with respect to the board. With what velocity does the board recoil?

In the figure given below, four identical circular rings of mass $10\text{kg}$ and radius $1\text{m}$ each, are lying in the same plane. The moment of inertia of the system about an axis through point $A$ and perpendicular to the plane of the rings is

A uniform circular disc of mass 200 g and radius 4.0 cm is rotated about one of its diameter at an angular speed of $10\frac{rad}{s}$. Find the angular momentum about the axis of rotation.

Force acting upon a charged particle kept between the plates of a charged condenser is F. If one plate of the condenser is removed, then the force acting on the same particle will become:

The light rays having photons of energy 1.8 eV are falling on a metal surface having a work function 1.2 eV. What is the stopping potential to be applied to stop the emitting electrons

A bomb at rest explodes into two fragments of mass 3 kg and 1 kg The total kinetic energy of fragments is 6×10⁴ J. Calculate kinetic energy of bigger fragment.

Water flows at a speed of 6 cm s^-1 through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. Is it a steady flow?

The value of contact angle for kerosene with solid surface.

Mercury violet light $(\lambda =4558\stackrel{\circ }{A})$ is falling on a photosensitive material $(\varphi =2.5eV)$. The speed of the ejected electrons is in $m{s}^{-1}$, about

Pressure of an ideal gas is obtained from kinetic gas equation. The kinetic gas equation is: $PV=\frac{1}{3}\left(m{N}_A\right)u^2=\frac{1}{3}M{u}^2$, where, $m{N}_A=M$(molar mass)

$N_A=\text{Avogadro's number}$

$u=\text{root mean square velocity}$

$\text{Translational kinetic energy of n mole}\frac{1}{2}M{u}^2=\frac{3}{2}\left(PV\right)=\frac{3}{2}\left(nRT\right)$

$\text{Average translational kinetic energy per molecule}=\frac{3}{2}\left(\frac{RT}{N_A}\right)=\frac{3}{2}\left(KT\right)$

$u_{rms}=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3P}{d}}$

and $u_{av}=\sqrt{\frac{8RT}{\pi M}}$

What is the rms speed of gas molecule of mass ${10}^{-12}$ gm at room temperature ${27}^{\circ }\text{C}$ according to kinetic theory of gases?

$(\text{Given}R=8J{K}^{-1}mo{l}^{-1},N_A=6\times {10}^{23})$

1. 196.35

A block released from rest from the top of a smooth inclined plane of inclination ${45}^{\circ }$ takes $t$ seconds to reach the bottom. The same block released from rest from the top of a rough inclined plane of the same inclination of ${45}^{\circ }$ takes $2t$ seconds to reach the bottom. The coefficient of friction is

A man can row a boat at $4km/h$ in still water. What is the minimum possible time in which he can cross the river if the speed of the current is $4km/h$ and the width of the river is $8km$?

The strain measurement from a rectangular strain rosette were ${\epsilon }_0=900\times {10}^{-6},{\epsilon }_{45}=750\times {10}^{-6}$ and ${\epsilon }_{90}=300\times {10}^{-6}$. The magnitude of minimum and maximum principal strain respectively is:

A $50\text{N}$ force is applied to the body of $2\text{kg}$. This applied force maintains the velocity of the body at $2\text{m/s}$. If the body moves in perpendicular direction to the applied force, find the power delivered by the force.

A wave is travelling in string 1 with velocity $v_1$. It is then both reflected and transmitted from a joint to string 2 where the velocity is $v_2$. If $A_i$ represents the incident amplitude, What are the reflected and transmitted amplitudes?

Monochromatic light of frequency ${\nu }_1$ irradiates a photocell and the stopping potential is found to be $V_1$. What is the new stopping potential of the cell if it is irradiated by monochromatic light of frequency ${\nu }_2$?

On a highway, the maximum speed of vehicles is $25\text{m/s}$. The material of the road provides a coefficient of friction of $0.2$. If the highway has a turn with a radius of curvature of $50\text{m}$, then what should be the banking angle for this turn to ensure the safety of the drivers?

Two parallel horizontal conducting wires are suspended by light vertical threads of length $75\text{cm}$. Each conductor has a mass of $40\text{g}$ per $\text{metre}$, and when there is no current they are $0.5\text{cm}$ apart. Equal current in the wires results in a separation of $1.5\text{cm}$. Find the value of current in the conductors.

Consider an ideal inverting op-amp circuit as shown in the figure below:



$\text{Both the resistance}{R}_1\text{and}{R}_2\text{are constructed with a tolerance of 5\%, then the range in which the gain of the amplifier can approximately vary is}$

Consider the force $F$ on a charge ${}^{\prime }{q}^{\prime }$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$, if ${}^{\prime }{q}^{\prime }$ is placed at distance $r$ from the centre of the shell?

A toroid has a mean radius $R$ equal to $\frac{10}{\pi }\text{cm}$, and a total of $200\text{turns}$ of wire carrying a current of $1.0\text{A}$. An alloy ring at temperature $27{}^{\circ }\text{C}$ inside the toroid provides the core. The magnetization $I_1$ is $7.2\times {10}^{-3}{\text{Am}}^{-1}$ for the alloy at $27{}^{\circ }\text{C}$. If the temperature of the alloy ring is raised to $87{}^{\circ }\text{C}$, then find the magnetization $\left(I_2\right)$ and susceptibility $\left({\chi }_2\right)$?

In a series RC circuit with an AC source, R = 300 $\Omega ,C=25\mu F$, ${ϵ}_0=50Vandv=\frac{50}{\pi }$ Hz. Find the peak current and the average power dissipated in the circuit.

A body covers the first $\frac{1}{3}$ part of its journey with the speed of $2m/s$, next $\frac{1}{3}$ part with the speed of 3 m/s and the rest of the journey with a speed $6m/s$. The average speed of the body will be

A lump of $0.10kg$ of ice at $-{10}^{\circ }C$ is put in $0.15kg$ of water at ${20}^{\circ }C$. How much water and ice will be found in the mixture when it has reached in thermal equilibrium.

(Specific heat of water $=1kcalk{g}^{-1}$, specific heat of ice $=0.50kcalk{g}^{-1}$ while its latent heat $=80kcalk{g}^{-1}$)

Water flows between two plates, of which the upper one is stationary and the lower one is moving with a velocity $V$. What will be the velocity of the fluid in contact with the upper plate?

A Hall effect material having thickness (t) = 2 mm is kept under $0.2wb/m{m}^2$ magnetic field strength. The Hall voltage is amplified using a non - inverting amplifier shown in the figure.



The current flowing through the Hall sensor is 4A. If the output $V_o$ of non inverting amplifier is 44 mV then the value of Hall co-efficient is

1. 166.2