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Two bodies of mass $0.4\text{kg}$ and $0.8\text{kg}$ move towards each other with initial velocities $5\text{m/s}$ and $2\text{m/s}$ respectively. After the collision, they stick together. Then, find the distance travelled by the combined mass, $12\text{sec}$ after the collision.

A $5\text{kg}$ block has a rope of mass $2\text{kg}$ attached to its underside and a $3\text{kg}$ block is suspended from the other end of the rope. The whole system is accelerated upward at $2{\text{ms}}^{-2}$ by an external force $F_0$.



What is the tension at middle point of the rope and $F_0$? $(g=10{\text{ms}}^{-2})$

Two rods of different materials having coefficients of thermal expansion ${\alpha }_1,{\alpha }_2$ and Young's modulii $Y_1,Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If ${\alpha }_1:{\alpha }_2=2:3$ and thermal stresses developed in the two rods are equal, then $Y_1:Y_2$ is equal to

Differentiation of $\frac{-x^3}{3}$ w.r.t $x$ is

A non-viscous liquid flows through a horizontal pipe of varying cross-sectional area. Identify the option which correctly represents the variation of height of rise of liquid in each vertical tube.

The potential energy for a conservative force system is given by $U=a{x}^3-bx$, where $a$ and $b$ are constants. Choose from the options, the correct $x$ coordinate(s) of the equilibrium position(s).

A small meteorite of mass 'm' travelling towards the centre of earth strikes the earth at the equator. The earth is a uniform sphere of mass 'M' and radius 'R'. The length of the day was 'T' before the meteorite struck. After the meteorite strikes the earth, the length of day increases (in sec) by

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

Adjoining figure shows the snapshot of two waves A and B at any time t. The equation for A is $y=Asin(kx-\omega t-\varphi )$, and for B it is y = A sin $(kx-\omega t)$. It is clearly shown in the figure that wave A is ahead of B by a distance $\frac{\varphi }{k}$.



The motion of a single point in time, i.e., y versus t for two waves is best represented by

Scientists of $ISRO$ want to achieve a velocity of rocket $100\text{m/s}$ after time $t=5\text{sec}$. Velocity of ejected burnt fuel is $20\text{m/s}$ w.r.t the rocket. What should be the rate of consumption of fuel (approximately) so that the rocket will achieve the desired velocity?

Initial mass of rocket is $2000\text{kg}$. [Take $g=10{\text{m/s}}^2$]

A car is moving with a speed of $60\text{m/s}$ on a curved road banked at an angle of ${45}^{\circ }$. If the coefficient of static friction between the wheels of the vehicle and the road is $0.4$, what should be the minimum radius of turn for the car so that it does not skid? Take $g=10{\text{m/s}}^2$.

Let $\omega$ be the angular velocity of the earth’s rotation about its axis. Assume that the acceleration due to gravity on the earth’s surface has the same value at the equator and at the poles. An object weighed at the equator gives the same reading as a reading taken at a depth $d$ below earth’s surface at a pole $(d<<R)$.The value of $d$ is

A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

The energy of a photon of wavelength $\lambda$ is given by

In a sinusoidal wave, the time required for a particle to move from maximum displacement to mean position is $0.17\text{s}$. The frequency of the wave is

The displacement time graph for two particles $A$ and $B$ are straight lines inclined at angles of ${30}^{\circ }$ and ${60}^{\circ }$ with the time axis. The ratio of velocities of $V_A:V_B$ is

A boat capable of running with velocity $v$ relative to water, in a flowing river having velocity as $u$. The boat travels a distance $d$ downstream and returns back to the original position. Find out the time taken in a complete trip.

If kinetic energy of a body is increased by 300%, then percentage change in momentum will be

A thin uniform rod of mass $5\text{kg}$ is rotating about an axis perpendicular to it's plane, passing through midpoint of the rod of length $4\text{m}$. Find the moment of inertia of the rod about this axis.

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

Two rods of length $L_1$ and $L_2$ are welded together to make a composite rod of length $(L_1+L_2)$. If the coefficients of linear expansion of the rod are ${\alpha }_1$ and ${\alpha }_2$ respectively, the effective coefficient of linear expansion of the composite rod will be

A large elevator is sliding on a wedge of angle $\theta$. What will be the range of a projectile in this frame, if it is projected at an angle $\alpha$

For the arrangement of mirrors as shown in the figure, a light ray is found to retrace its path when the angle of incidence on the plane mirror is ${30}^{\circ }$. Find the distance $OP$, if focal length of concave mirror is $25\text{cm}$.

A ball of mass $5\text{kg}$ is dropped from a tower. Find the power of gravitational force at time $t=2\text{seconds}$.

(Take $g=10{\text{m/s}}^2$)

A point object $O$ is moving with a velocity of $v$ in front of an arrangement of plane mirrors as shown in the figure. The magnitude of velocity of image in mirror $M_1$ with respect to the image in mirror $M_2$ will be

A system of units uses force $\left(F\right)$, acceleration $\left(A\right)$ and time $\left(T\right)$ as their fundamental physical quantities. The dimension of length in the system is

Two bodies A (of mass $1\text{kg})$ and B (of mass $3\text{kg})$ are dropped from heights of $16\text{m}$ and $25\text{m}$, respectively. The ratio of the time taken by them to reach the ground is

In a physics lab, we took two readings of dip angle by dip circle, in two readings planes of dip circle are mutually perpendicular, then ratio of vertical & horizontal component of field the to earth in lab is (reading 1 = ${45}^0$ reading 2 = ${60}^0$)

If $\overrightarrow{A}=4\hat{i}-3\hat{j}$ and $\overrightarrow{B}=6\hat{i}+8\hat{j}$ then magnitude and direction of $\overrightarrow{A}+\overrightarrow{B}$ will be

A motor car moving with a uniform speed of $20m{s}^{-1}$ comes to rest on the application of brakes after travelling a distance of 10 m. Its acceleration is

A car is moving with a velocity of $20\text{m/sec}$. The driver sees a stationary truck at a distance of $100\text{m}$ ahead. After some reaction time $\Delta t$ he applies the brakes, produces a retardation of $4{\text{m/s}}^2$. The maximum reaction time to avoid collision will be

The phase difference between two points separated by $0.8\text{m}$ in a wave of frequency $120\text{Hz}$ is $0.5\pi$. The velocity of wave will be

The figure shows a spherical concave mirror of radius of curvature $R=10\text{cm}$, with its pole at $(0,0)$ and principal axis along $x-$axis. There is a point object $O$ at $(-40\text{cm},1\text{cm})$. The position of the image is :

What is the acceleration of the block?

A block of mass 'm' moving with speed 'v' collides with another block of mass '2m' which was at rest. The lighter block comes to rest after the collision. The coefficient of restitution is

What is the magnetic field $\overrightarrow{dB}$ at a distance $\overrightarrow{r}$ due to a small current element $\overrightarrow{dl}$ carrying current I?

At what angular speed the Earth should rotate, so that effective acceleration due to gravity at ${45}^{\circ }$ latitude becomes half of effective acceleration due to gravity at pole? (Radius of earth is $R$ and acceleration due to gravity without taking variation of Earth’s rotation at surface is $‘g^{\prime }$)

Two particles of masses $m_1$ & $m_2$ and velocities $u_1$ and $\left(\alpha u_1\right)(\alpha \ne 0)$ make an elastic head on collision. If the initial kinetic energies of the two particles are equal and $m_1$ comes to rest after collision, then

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $R^{\frac{-5}{2}}$, then

Three particles, each of mass m, are placed at the vertices of an equilateral triangle of side a. The gravitational field intensity at the centroid of the triangle is

If a car covers $2/5^{th}$ of the total distance with $v_1$ speed and $3/5^{th}$ distance with $v_2$ then average speed is

A car of mass $m=1000\text{kg}$ is moving with constant speed $v=10\text{m/s}$ on a parabolic shaped bridge $AFOE$ of span $l=40\text{m}$ and height $h=20\text{m}$ as shown in the figure. Then the net force applied by the bridge on the car, when it is at point $F$ is :



Assume $g=10{\text{ms}}^{-2}$

A projectile is fired from the surface of the earth with a velocity of $5{\text{ms}}^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3{\text{ms}}^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in${\text{ms}}^{-2})$ is

(Given $g=9.8{\text{ms}}^{-2}$)

Two wires A and B of the same material have their lengths in the ratio of 1:2 and their diameters in the ratio of 2:1. If they are stretched with the same force, the ratio of the increase in the length of A to that of B will be

A rod of length $6\text{m}$ is placed along the $x-$ axis between $x=0$ and $x=6\text{m}$. The linear density (mass/length) $\lambda$ of the rod varies with the distance $x$ from the origin as $\lambda =k(10-x)$. Here $k$ is a positive constant. Find the position of the centre of mass of this rod.

A source of emf $E=10\text{V}$ and having negligible internal resistance is connected to a variable resistance. The resistance varies as shown in figure. The total charge that has passed through the resistor $R$ during the time interval from $t_1$ to $t_2$ is

Which of the following options correctly represent the $FBD$ of the block for the figure shown?

An ice block at $0^{\circ }\text{C}$ and of mass $m$ is dropped from height ${}^{\prime }{h}^{\prime }$ such that the loss in gravitational potential energy of the block is exactly equal to the heat required to completely melt the ice. Taking latent heat of fusion of ice, $L=80\text{cal/gm}$, acceleration due to gravity $g=10{\text{m/s}}^2$ and mechanical equivalent of heat $J=4.2\text{J/cal}$. find the value of ${}^{\prime }{h}^{\prime }$.