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A disc having radius $r=1\text{m}$ and $m=2\text{kg}$ is rotating about an axis passing through its COM and perpendicular to the plane of disc. Initial velocity of a point $A$ at the edge of disc is $6\text{m/s}$. A retarding torque of magnitude $2\text{Nm}$ starts acting on disc about its axis of rotation. Find the velocity of point $A$ after $t=2\text{s}$.

The length of a simple pendulum is $32\text{cm}$. It is suspended by the roof of a lift which is moving upwards with an acceleration of $6.2{\text{m/s}}^2$. Find the time period of pendulum.

A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

A particle starts from rest and undergoes an acceleration as shown in the figure. The velocity -time graph from the figure will have a shape

In a young's doube slit experiment using mono-chromatic light, the fringe pattern shifts by a certain distance on the screen whwen a mica sheet of refractive index 1.6 and thickness 1.964 micron $(1micron={10}^{-6}m)$ is introduced in t epath of one of th einterfering waves. The mica sheet is then removed and
the distance between the screen and the slits is doubled. It is found that the distance between teh successive maxima now is the same as the observed fringe- shift upon th eintroduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment.

Nuclear radius of ${}^{27}Al$ is $3.6\times {10}^{-15}\text{m}$, approximate radius of ${}^{64}Cu$ is

A voltmeter consists of a 25 $\Omega$ coil connected in series with a 575 $\Omega$. The coil takes 10mA for full scale deflection. What maximum potential difference can be measured on this voltmeter ?

A two dimensional lamina of arbitrary shape is placed in $x-y$ plane as shown in the figure. $\text{MOI}$ of lamina about $x$ and $y$ axes are $I_x=6{\text{kg-m}}^2$ and $I_y=4{\text{kg-m}}^2$ respectively. If point of intersection $\left(O\right)$ of the axes does not lies on lamina, then the $\text{MOI}$ of lamina about $z$ axis i.e. $\left(I_z\right)$ will be

Two small balls A and B, each of mass m, are attached rigidly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed $\omega$. The angular momentum of the system about the axis of rotation is .

A vertical U – tube of uniform cross – sectional area A contains a liquid of density $\rho$ The total length of the liquid column in the tube is L. the liquid column is disturbed by gently blowing into the tube. If viscous effects are neglected, the time period of the resulting oscillation of the liquid column is given by

A bead of mass$\frac{1}{2}kg$ which is at rest, starts to move from end A of a smooth fixed quarter ring of radius $5m$ in vertical plane under the action of a constant horizontal force $F=5N$ as shown. Then the speed of the bead as it reaches the end B is

Average velocity of a particle moving in a straight line, with constant acceleration ‘a’ and initial velocity u in first t seconds is :

A metallic bob of mass ‘$m$’ attached to a string, is raised through a height of $50\text{cm}$ and released. At what distance along the vertical from the point of suspension should a nail be placed so that the bob just completes a circle with the nail as the centre?

Three rings each of mass M and radius R are arranged as shown in the figure. The moment of inertia of the system about YY' will be

The elevator shown in the figure is descending with an acceleration of $2m/s^2$. The mass of the block $A=0.5\text{kg}$. The force exerted by the block $A$ on the block $B$ is (take $g=10{\text{m/s}}^2$)

The mass of a rocket is $2400\text{kg}$. The nozzle of the rocket is designed to give velocity of $200\text{m/s}$ to the gases produced after combustion of the fuel. If the rocket has to achieve an acceleration of $15{\text{m/s}}^2$, what should be the rate of burning of the fuel? (Take $g=10{\text{m/s}}^2$)

What would be the work done by the gas if the entire process is reversed (3 - 2 - 1)?

Consider a uniform annular sphere of density $\rho$ and radius $2m$ and external radius $4m$. The gravitational field strength at a point at a distance $r=3m$, from the centre of the sphere is

Kirchhoff's first law is based on

Two particles are projected from the ground simultaneously with speeds $20m/s$ and $20m/s$ at angles ${30}^{\circ }$ and ${60}^{\circ }$ with the horizontal in the same direction. The maximum distance between them till both of them strike the ground is approximately ($g$ = $10m/s^2$)

A disc of radius $0.1\text{m}$ rolls without sliding on a horizontal surface with a velocity of $6\text{m/s}$. It then ascends a smooth continuous track as shown in figure. The height upto which it will ascend is $(g=10{\text{m/s}}^2)$.

The v-s and $v^2$-s graph are given for two particles. Find the acceleration of the particles at s=0

By what percent the energy of a satellite has to be increased to shift it from an orbit of radius r to $\frac{3}{2}r$?

Which of the following relation is correct with respect to the angle with the horizontal at which an object should be projected so that the maximum height reached is equal to the horizontal range ?

Figure shows a square plate of uniform thickness and side length $\sqrt{2}$m. One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

A boat of mass $M=100\text{kg}$ and length $L=20\text{m}$ is on a frictionless water surface. Two men $A$ of mass $m_1=25\text{kg}$ and $B$ of mass $m_2=50\text{kg}$ are standing at the two opposite ends. Now, both start travelling in opposite directions to each other and they reach the opposite positions of each other. Find the distance travelled by the $A$ w.r.t the ground.

The length of a rod is $20cm$ and area of cross-section $2c{m}^2$ . The Young's modulus of the material of wire is $1.4\times {10}^{11}N{m}^{-2}$. If the rod is compressed by $5kg-wt$ along its length, then increase in the energy of the rod in joules will be

A heavy plank of mass 100 kg hangs on three vertical wires of equal length arranged symmetrically (see fig.). The middle wire is of steel and the other two are of copper. All the wires have the same cross-section. The modulus of elasticity of steel is twice that of copper. The tensions in the copper and steel wires are respectively

A body is moving with uniform acceleration starting from rest.
Match column I with Column II.
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{a. Its velocity at the end of t sec., 2t sec., 3t sec. etc are in the ratio}& \text{p.}1:2:3\\ \text{b. Distances covered in}{1}^{st}\text{t sec.,}& \text{q.}1:1:1\\ 2^{nd}\text{t sec}.,3^{rd}\text{t. sec. are in the ratio}& \\ \text{c. Distances covered in t sec., 2t sec \&}& \text{r.}1:3:5\\ \text{3t sec. are in the ratio}& \\ \text{d. Change in velocity at the end of}& \text{s.}1:4:9\\ 1^{st}\text{t.sec}.,2^{nd}\text{t.sec}.,3^{rd}\text{t.sec are in the ratio}& \end{array}$

A ray of light incidents on a plane mirror at an angle ${30}^{\circ }$, calculate the angular deviation of the reflected ray.

The displacement of a particle varies with time $t$ as: $s=\alpha t-\beta t^2$. Determine the time $\left(t\right)$ at which velocity of the particle becomes $0$.

It is desired to increase the volume of 80 $c{m}^3$ of a gas by 20% without changing pressure. To what temperature the gas be heated if its initial temperature is ${25}^{\circ }C$?

Two particles execute S.H.M. of same amplitude and frequency along the same straight line. They pass one another when going in opposite directions. Each time their displacement is half of their amplitude. The phase difference between them is

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be

Which of the following gates will have an output of 1

A ball of radius r and density $\rho$ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is n, the value of h is given by

Two wires A and B of same length and of the same material have the respective radii $r_1$ and $r_2$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

A uniform cubical block of density ${\rho }_b\left(\text{in g/cc}\right)$ and length a is released from rest from the position where one of its horizontal surface (lower) just touches the water (density ${\rho }_w=1\text{g/cc}$). The time period of oscillation of the block is $({\rho }_b=\frac{2}{3}\text{g/cc},\text{neglect viscosity and surface tension})$

If $\overline{a},\overline{b}$ are not perpendicular to each other and $\overline{r}\times \overline{b}=\overline{c}\times \overline{b},\overline{r}.\overline{a}=0,then\overline{r}=$

Two identical glass rods $S_1$ and $S_2$ (refractive index = 1.5) have one convex end of radius of curvature $10cm$. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light $P$ is placed inside rod $S_1$ on its axis at a distance of $50cm$ from the curved face, the light rays emanating from it are found to be parallel to the axis inside $S_2$. The distance $d$ is

As shown in figure string PQR is stretched by force F = (3 –10 Kt) N, where k is a constant and t is time in second. At time t = 0, a pulse is generated at the end P of the string. Find the value of K (in N/s) if the value of force become zero as the pulse reaches point Q.(linear density of string is $3\times {10}^{-2}kg{m}^{-1}$)

Four identical charged particles having same mass are located at four corners of a regular tetrahedron. If only one of the particles is released, with the remaining tetrahedron fixed, it acquires a final speed of $V_o.$ If all the charges are released together, their final speed will be $\frac{V_o}{n}$, then n is