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A block of mass M is being pulled along rough horizontal surface. The coefficient of friction between the block and the surface is $\mu$. If another block of mass M/2 is placed on the block and it is again pulled on the surface, the coefficient of friction between the block and the surface will be

Find the charge on the capacitor $C=1\mu F$
in the circuit shown.

Find the dimensional formulae of the capacitance C

Some of the equations containing these quantities are

Q = It, U = VIt, Q = CV and V = RI;

Where 'I' denote the electric current, 't' is time and 'U' is energy.

Energy has the dimension of Force x displacement

Two cars A and B are travelling in the same direction with velocities $v_1$ and $v_2(v_1>v_2)$ When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

A body of mass $100\text{grams}$ is allowed to fall freely under gravity. Find its momentum after $10$ seconds (in $\text{N- s}$)

A cylindrical piece of cork of height $h$ and density ${\rho }_c$ floats vertically in a liquid of density ${\rho }_l$ The cork is depressed slightly and released. If viscous effects are neglected, the time period of vertical oscillations of the cylinder is given by

Figure shows a loop track of radius $r$. A box starts sliding from a platform at a distance ($h$) above the top of the loop and goes around the loop without falling off the track. Find the minimum value of $h$ for a successful looping. Friction is negligible at all surfaces.

A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence ${45}^{\circ }$.The ball is reflected by the plane at equal angle of reflection with the same speed.Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.

A gas will approach ideal behaviour at:

A boy standing at the top of a tower of $20\text{m}$ height drops a stone. Assuming $g=10{\text{ms}}^{-2}$ the magnitude of velocity with which it hits the ground is

Which of the given relation is true for molar heat capacity of a substance?

Two identical stringed instruments have frequency 100 Hz. If tension in one of them is increased by 4% and they are sounded together then the number of beats in one second is

If acceleration of block A is a rightward, then acceleration of block B will be:

A chain of mass $m$ and length $l$ is placed on a table with one-sixth of it hanging freely from the table edge. The amount of work done to pull the chain on to the table is

A straight horizontal conducting rod of length 0.5 m and mass 50 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? Ignore the mass of the wires and take g = 10 $m{s}^{-2}$.

Figure shows two adiabatic vessels each having $m\text{gm}$ of water at different temperatures. The ends of a metal rod of length $L$, area of cross section $A$, and thermal conductivity $K=\frac{msL}{2A}$ [where $s$ is the specific heat capacity of water] are connected to the water in the vessels as shown in the figure. Find the time taken for the difference in temperature of the vessels to become half of the original value.

A truck of mass $2000kg$ travelling at $4\text{m/s}$ comes to rest in $2\text{s}$ when it strikes a wall. Force exerted by the wall is

A straight conducting rod $PQ$ is executing $\text{SHM}$ in $xy-$plane from $x=-d$ to $x=+d$. Its mean position is $x=0$ and its length is along $y-$ axis. There exists a uniform magnetic field $B$ from $x=-d$ to $x=0$ pointing inward normal to the paper and from $x=0$ to $=+d$ there exists another uniform magnetic field of same magnitude $B$ but pointing outward normal to the plane of the paper. At the instant $t=0$, the rod is at $x=0$ and moving to the right. The induced emf $\left(\epsilon \right)$ across the rod $PQ$ vs time $\left(t\right)$ graph will be

A laser beam has intensity $2.5\times {10}^{14}$ W $m^{-2}$ Find the amplitudes of electric and magnetic fields in the beam.

A particle of mass $2\text{kg}$ is moving in $xy$ plane. Its velocity and acceleration at a certain instant of time is given by $\overrightarrow{v}=(3\hat{i}+4\hat{j})\text{m/s}$ and $\overrightarrow{a}=(5\hat{i}+4\hat{j}){\text{m/s}}^2$. Find the power delivered by force at that instant of time.

A ball is thrown such that it strikes the ground with velocity $v_0$ making an angle $\theta$ with the vertical. The height to which it rises after the collision (if the coefficient of restitution is $e$) is

The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height $h$ from rest without sliding is

Why does a current-carrying conductor in a magnetic field experience force? On what factors does the direction of this force depend on? Name and state the rule used for determination of the direction of this force.

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area
A = 10cm${}^2$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is

The number of degrees of freedom of a triatomic gas is

A particle of mass $m$ is located at point O. Find $I_A,I_B,I_{AB}$ and $I_{A{A}^{\prime }}$ respectively.

A hollow spherical ball of radius $2\text{m}$ and mass $3\text{kg}$ is rotating about a fixed axis passing through its COM. If it has kinetic energy of $576\text{J}$, the angular speed of the hollow spherical ball about the fixed axis is

Consider the situation shown in figure (17-E6). The two slits $S_1$ and $S_2$ placed symmetrically around the central line are illuminated by a monochromatic light of wavelength $\lambda$ the separation between the slits is d. The light transmitted by the slits falls on a screen ${\sum }_1$ placed at a distance D from the slits. The slit$S_3$ is at the central line and the slit $S_4$ is at a distane z rom $S_3$ Another screen ${\sum }_2$ is palced a further distance D away from ${\sum }_1$ find the ration of thmaximum to minimum intensity obsered on ${\sum }_2$ if z is equal to
(a) $z=\frac{\lambda D}{2d}$
(b) $\frac{\lambda }{d},$
(c) $\frac{\lambda D}{4d}.$

In the following figure, the p.d. between the points $M$ and $N$ is balanced at $50\text{cm}$. length. The length in $\text{cm}$, balancing for the potential difference between points $N$ and $C$ will be –

A pendulum clock gives correct time at ${20}^{\circ }C$ at a place where g = 9.800 $m{s}^{-2}$. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g 9.788 $m{s}^{-2}$. At what temperature will it give correct time ? Coefficient of linear expansion of steel $=12\times {10}^{-6}{}^{\circ }{C}^{-1}$

In the adjacent diagram, CP represents a wavefront and AO and BP, the corresponding two rays. Find the condition on $\theta$ for constructive interference at P between the ray BP and reflected ray OP

A battery of internal resistance $4\Omega$ is connected to the network of resistances as shown in the figure. In order that the maximum power can be delivered to the network, the value of 𝑅 in $\Omega$ should be

The velocity at the maximum height of a projectile is half its initial velocity of projection. Find its range on the horizontal plane. If $u=20{\text{ms}}^{-1}$. (Take $g=10{\text{m/s}}^2$)

What is the meaning of the sentence'the acceleration of the particle is bounded'

A spring has natural length of $50\text{cm}$ and a force constant of $2.0\times {10}^3{\text{Nm}}^{-1}$ . A body of mass $10\text{kg}$ is suspended from it in equilibrium position. If the body is pulled down, such that length of spring becomes $58\text{cm}$ and released. If it executes simple harmonic motion, what is the net force on the body, when it is at it's lowermost position of oscillation ?
$(\text{Take g}=10{\text{ms}}^{-2})$.

In the shown circuit, potential difference between points A and B is 16 V. The current passing through 2W resistor will be :

An engine pumps up 100 kg water through a height of 10 m in 5s. Given that the efficiency of the engine is 60%. If g = 10 m/s², then the power of the engine is

The length of the wire between the pulleys is $1.5\text{m}$ and its mass is $12\text{gm}$. Find the frequency of vibration, with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.
Use value of $\sqrt{11250}\approx 106$

In figure, a square loop consisting of an inductor of inductance L and resistor of resistance R is placed between two long parallel wires. The two long straight wires have time varying current of magnitude
$I=I_{0}cos\omega t$ but the direction of current in them are opposite.

Total magnetic flux in this loop is

A particle of mass $10\text{g}$ moves along a circle of radius $6.4\text{cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle is equal to $8\times {10}^{-4}\text{J}$, by the end of the second revolution (after the beginning of the motion)?