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The blocks shown in figure (9-E19) have equal masses. The surface of A is smooth but that of B has a friction coefficient of 0.10 with the floor. Block A is moving at a speed of 10 m/s towards B which is kept at rest. Find the distance travelled by B if (a) the collision is perfectly elastic and (b) the collision is perfectly inelastic. Take $g=10m/s^2.$

A cuboidal block is kept in a groove. The groove is made to rotate with angular acceleration $\alpha$ . Find the magnitude of the normal reaction on block by the walls of groove given the blocks mass is mkg and it is kept at a distance of r from the axis of rotation.

Two large conducting sheets are kept parallel to each other as shown in the figure. In equilibrium, the charge density on facing surfaces is ${\sigma }_1$ and ${\sigma }_2$. What is the net value of electric field at $\text{A}$ ?

A car of mass $\text{1000 kg}$ moving with a velocity of $\text{20 m/s}$ is brought to rest by applying brakes in $\text{10 seconds}$. What is the force applied by the brakes?

In the given figure, the load weighs 200N, $\theta$=${37}^{\circ }$ and beam has negligible mass. Then, the tension in string and horizontal and vertical forces that pivot exerts on the beam is

What is the distance of the body from the starting point at t = 30 s?

What is the distance of the body from the starting point at t = 30 s?

A body is moving down along an inclined plane of an angle of inclination $\theta$. The coefficient of friction between the body and the plane varies as $\mu =0.5x$, where $x$is the distance moved down the plane. The body will have the maximum velocity when it has traveled a distance x given by

Consider a spherical conductor with an irregularshaped cavity inside it with no charge inside thecavity. If this conductor is placed in an externalelectric field then Which of the following is correct

(a) Net electric field inside the cavity will not be zero

(b) No net charge will induced on inner and outer surface of the conductor

(c) Electric field lines will not be found inside the cavity as well as in the conductor

(d) Electric field and potential inside the cavity will be zero

(1) a, b and d (2) a and c (3) b and c only (4) only d

A cubical wooden block of side L and relative density 0.5 is floating on the surface of water as shown in the figure. A string is attached by a pulley to it as shown. The graph of tension T in the string versus distance of the bottom of the block from the free surface of water when the end A of the rope is slowly being pulled up will be (block is moving)

A long solid non-conducting cylinder of radius $10\text{cm}$ contains a uniformly distributed charge of density $10{\text{nC/m}}^3$. Find the magnitude of electric field at a point $\text{P}$ inside the cylindrical volume at a distance $5\text{cm}$ from its axis.

(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

A body is at rest at $x=0$. At $t=0$, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive x-direction with a constant speed. The position of the first body is given by $x_1\left(t\right)$ after time $t$ and that of the second body by $x_2\left(t\right)$ after the same time interval. Which of the following graphs correctly describes $(x_1-x_2)$ as a function of time $t$?

A layer of benzene $({\mu }_1=1.5)6\text{cm}$ deep floats on water $({\mu }_2=1.3)4\text{cm}$ deep. When viewed vertically through air the apparent distance of the bottom of the vessel below the surface of the benzene will be -

Two particles move along x axis. the position of particle 1 is given by x = 6.00$t^2$ + 3.00t + 2.00 (in meters and seconds); the acceleration of particle 2 is given by a = -8.00t ( in meters per second squared and seconds) and, at t = 0, its velocity is 19 m/s. When the velocities of the particles match, what is their velocity?

Write the dimensions of $(a\times b)$ in the relation $E=\frac{b-x^2}{at}$, where $E$ is the energy, $x$ is the displacement and $t$ is time.

The set of all points, where $f\left(x\right)=\sqrt[3]{3x^2|x|}-\frac{|x|\sqrt{1-{\cos }^{2}2x}{\sec }^{2}x}{2\tan x}-1$ is not differentiable is

A proton is accelerating in a cyclotron. It comes out of the cyclotron with the kinetic energy $K$. If it is required to have kinetic energy $4K$, then the radius of the circular path will be _____ times of its initial value.

If a force $F=(3\hat{i}+4\hat{j}+5\hat{k})N$ is acting on a particle moving on a circle of radius $2m$ with a speed increasing at the rate of $2m/s^2$. All points on the circle satisfy the equation $3x+4y+5z=0$. The power due to the force on the particle is

A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.





The potential of outer shell is:

A liquid of density d is pumped by a pump p from situation (i) to situation (ii) as shown in the diagram. If the cross-section of each of the vessels is a, then the work done in pumping (neglecting friction effects) is

Magnitude of vector which comes on addition of two vectors, $6\hat{i}+7\hat{j}$ and $3\hat{i}+4\hat{j}$ is

From the top of a tower, a particle is thrown vertically downwards with a velocity of $10m/s$. The ratio of distances covered by it in the $3^{rd}$ and $2^{nd}$ seconds of its motion is (Take $g=10m/s^2$)

A steel ring of radius r and cross-section area 'A' is fitted on to a wooden disc of radius R(R$>$ r). If Young's modulus be E, then the force with which the steel ring is expanded is

The phase space diagram for a ball thrown vertically up from ground is

If the angle between incident beam and crystallographic plane is ${30}^{\circ }$, then the scattering angle is -

At a given instant, block A is moving upwards with velocity of $5m/s$. What will be velocity of block B at that instant ?

(Take upward velocity to be positive.)

Recently, the phenomenon of superconductivity has been observed at 95 K. This temperature is nearly equal to

A thin film of soap solution of refractive index $\mu$ and thickness t appears shining by a normal reflected light wavelength $\lambda$ then t can be

In a turbulent pipe flow, root-mean-square (RMS) values of velocities in 3D directions are



$\overline{u^1}=10m/s$

$\overline{v^1}=20m/s$

$\overline{w^1}=45m/s$



The degree of turbulence velocity value is

A ball is projected from the ground at a speed of $10m{s}^{-1}$ making an angle ${30}^{\circ }$ with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. Both the balls collide at the maximum height of the projectile. What was the initial height of the freely falling body?( Assume $g=10m{s}^{-2}$)

A current $I$ flows through a flat metal specimen of constant thickness and of the shape as shown in the figure. Given that $v_1,v_2$ and $v_3$ are mean drift speeds of the electron crossing the sections $P_1,P_2$ and $P_3$ respectively. Then