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Find the total impulse acting on a body up to 8 seconds from the $F-t$ graph shown.

A ray of light is incident at an angle $i$ on a surface of a thin prism of angle $A$, which emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, the angle of incidence $i$ is nearly equal to :

At room temperature, the number of degrees of freedom of linear diatomic molecule is

A road is 10 m wide. Its radius of curvature is 50 m. The outer edge is above the lower edge by a distance of 1.5 m. This road is most suited for the velocity

If the velocity time graph is some straight line parallel to the x axis, then definitely

A force $F$ is applied to a block of mass $4\sqrt{3}\text{kg}$ as shown in the diagram. What should be the maximum value of force so that the block does not move?

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

A car travel first $\frac{1}{3}rd$ of the total distance at $30\text{km/hr}$, next $\frac{1}{3}rd$ of the total distance at $40\text{km/hr}$ and last $\frac{1}{3}rd$ of the total distance at $24\text{km/hr}$. It's average speed in $\text{km/hr}$ for the whole Journey is

A man places a chain (of mass ${}^{\prime }{m}^{\prime }$ and length ${}^{\prime }{L}^{\prime }$) on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is:

Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures $T_1$ and $T_2$, rod $1$ takes twice the time as the other. Find the ratio of their lengths.

A small spherical body of radius $r$ is falling under gravity in a viscous medium and due to friction, the medium gets heated. When the body attains terminal velocity, then the rate of heating is proportional to:

Blocks B and C are connected by a single inextensible cable, with this cable being wrapped around pulleys at D and E. In addition, the cable is wrapped around a pulley attached to block A as shown. Assume the radii of the pulleys to be small. Blocks B and C move downward with speeds of $V_B=6ft/s$ and $V_C=18ft/s,$ respectively. Determine the velocity of block A when $S_A=4ft.$

Find the velocity of images formed due to a point object $O$ w.r.t. ground if the mirror is at rest. All speeds given are w.r.t a stationary ground observer

The voltage across an inductor is given by

Two men $(A$ & $B)$ of mass $50\text{kg}$ and $100\text{kg}$ are standing at the two opposite ends of a boat of mass $200\text{kg}$ and length $L=20\text{m}$. $A$ travels a distance $5\text{m}$ right relative to the boat towards the centre and $B$ moves a distance $15\text{m}$ left relative to the boat and meets $A$. Find the distance travelled by the boat in the water when they meet.

A closed tube is filled with liquid $\rho =800{\text{kg/m}}^3$. It is rotating about an axis shown in figure with an angular velocity $\omega =4\text{rad/sec}$ and length of the tube is $9\text{m}$. Find the pressure difference between the ends of the tube.

For the wave shown in figure, write the equation of this wave if its position is shown at t = 0. Speed of wave is v = 30 m/s.

A particle moves along the positive x-axis from origin with velocity, $V_0$ = 2m/s and a = 6(t - 1) where't' is in seconds. Which of these graphs are correct?

A body at rest starts moving under the action of a constant force along a straight line. The instantaneous power developed by this force with time $\text{t}$ is correctly represented by

If a particle moves in a circle describing equal angles in equal times, its velocity vector

Which of the following relationships between the acceleration $a$ and the displacement $x$ of a particle implies simple harmonic motion?

To excite an electron from one orbit to another we need:

Spherical sound waves are emitted uniformly in all directions from a point source. The variation in sound level SL as a function of distance ‘r’ from the source can be written as

Where a and b are positive constants.

Which of the following diagram correctly represents the working of a Carnot's refrigerator?

A streetcar moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $f=a-bx$, where $a$ and $b$ are constant, and $x$ is the distance from station $A$. The distance between the two stations and maximum velocity are

Kerosene oil is flowing through a pipe having constant cross section area with diameter $2.5\text{cm}$, at a rate of $10\text{litre/sec}$. The height of bottom and top end is $2\text{m}$ and $8\text{m}$ respectively from the datum line. Find the pressure at the lower end, if the pressure at the other end is $25\times {10}^4{\text{N/m}}^2$. (Density of kerosene $=850{\text{kg/m}}^3)$

Train $A$ travelling at $60\text{km/h}$ overtakes another train $B$ travelling at $42\text{km/h}$. Assuming each train to be $50\text{m}$ long and initially train $A$ to be just behind the train $B$, the total road distance used for the overtake is closest to

Find the height by which the sphere rises when the wedge touches the wall. Let the initial distance between the wedge and the wall is $10\text{m}$ and the wedge is moved to the left until it touches the wall. (Assume all surfaces to be smooth)

The sum of the numbers $436.32,227.2$ and $0.301$ in appropriate significant figures is

If $2$ moles of an ideal monoatomic gas at temperature $T_0$ is mixed with $4$ moles of another ideal monoatomic gas at temperature $2T_0$, then the temperature of the mixture is

As shown in the figure, a truck has its rear side open and a box of $40\text{kg}$ mass is placed $5\text{m}$ away from the open end. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road, the truck starts from rest and accelerates with $2{\text{m/s}}^2$. Find the distance (in metres) travelled by the truck by the time the box falls from the truck. (Ignore the size of the box). [Take $g=10{\text{m/s}}^2$]

A ring shaped object of radius $R$ contains mass $M$ distributed non-uniformly. Which of the following graphs correctly represents the variation of gravitational potential at a point on the axis of ring?

(Assume that ring is in YZ plane with origin as centre)

A block of mass M slides along the sides of a bowl as shown in the figure. The walls of the bowl are frictionless and the base has coefficient of friction 0.2. If the block is released from the top of the side, which is 1.5 m high, where will the block come to rest ? Given that the length of the base is 15 m

In the given constraint, if the string is inextensible and pulley is frictionless, then magnitude of velocity of block $A$ $\left(V_A\right)$ is

A metallic bob of weight $100\text{gm}$ is suspended in air. If it is immersed in a liquid at temperature of ${30}^{\circ }\text{C}$, it weighs $90\text{gm}$. When the temperature of the liquid is raised to ${100}^{\circ }\text{C}$, it weighs $90.2\text{gm}$. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is $15\times {10}^{-6}/{}^{\circ }\text{C}$

A block of mass $m$ is at rest on a rough wedge of angle $\theta$ as shown. What is the force exerted by the wedge on the block?

Two masses m and 2m are joined to each other by means of a frictionless pulley as shown below. When the mass 2m is released, the mass m will ascend with an acceleration of

A light ray goes from a medium of refractive index$\sqrt{2}$ to a medium of refractive index 1. The minimum angle of incidence for TIR to happen is .

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at $t=0$), the car was at $x=0$, where, $x$ is the position of the car at any time ‘$t$’.



The maximum displacement from the starting position will be

An iron tyre is to be fitted onto a wooden wheel 1.0 m in diameter. The diameter of the tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (Coefficient of volume expansion of iron is $3.6\times {10}^{-5}{/}^{\circ }C$)

The displacement $x$ of a particle along a straight line at time $t$ is given by $x=a_0–a_{1}t+a_2{t}^2$. The acceleration of the particle is:

Find the tension in the string and the acceleration of the blocks?

An air bubble of diameter $4\text{mm}$ rises steadily through a solution of density $1800{\text{kg/m}}^3$ at the rate of $0.05\text{m/s}$. Neglecting density of air, the co-efficient of viscosity of the solution is

[Take $g=10{\text{m/s}}^2$]

A swimmer wishes to cross a river that is $500m$ wide flowing at a rate $u$. For this, he makes an angle $\theta$ with the vertical to the direction of flow of the river as shown. His speed with respect to still water is $v$. In order to cross the river in minimum time, the value of $\theta$ in degrees should be

In the previous question, R is:

Calculate the ratio of the speed of sound in neon to that in water vapour at any given temperature.

[molecular weight of neon $=2.02\times {10}^{-2}\text{kg/mol}$ and of water vapour $=1.8\times {10}^{-2}\text{kg/mol}$. Given that water vapour is triatomic]

In a horizontal spring mass system, mass $m$ is released after being displaced towards right by some distance at $t=0$ on a frictionless surface. The phase angle of the motion in radian when it passes through the equilibrium position for the first time is

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river flow. If AB = BC = 400 m. At what angle with river bank should swimmer swim?

A disc is having an initial angular velocity of $4\text{rad/sec}$ and angular acceleration of $8{\text{rad/sec}}^2$. Find the angle rotated (in radian) by disc in $3\text{sec}$.

A car of mass $1000\text{kg}$ moves in a circular path with a constant speed of $16\text{m/s}$. It is turned by ${90}^{\circ }$, while travelling a distance of $628\text{m}$ on the road. The centripetal force acting on the car is