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In which of the following cases, the rays after reflection from a concave mirror diverge:

A cylinder of capacity 20 litres is filled with $H_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5\times {10}^{5}J$. The pressure of hydrogen in the cylinder is

If the speed of a particle is given as $v=6t^2+2t\text{m/s}$, the speed of the particle at $3\text{sec}$ and the average speed in $4\text{sec}$ respectively is

A particle is sticked to a disc at a distance $\frac{r}{2}\text{m}$ from centre. Disc has initial angular velocity of ${\omega }_o=6\hat{j}\text{rad/s}$ and constant angular acceleration of $\alpha =-\hat{j}{\text{rad/s}}^2$ as shown in figure. If radius of disc is $1\text{m}$, find the speed of particle after $t=2\text{s}$.

What is the power required by the pump to lift $1000\text{kg}$ of water per minute from a $20\text{m}$ deep well and eject it with the speed of $20\text{m/s}$?

Coefficient of friction between two blocks is $\mu =0.6$. The blocks are given velocities in the directions shown in the figure below. Find the common velocity attained by both the blocks. [Take $g=10{\text{m/s}}^2$]

The acceleration time graph for the object whose displacement time graph is shown below is?

If nitrogen gas molecules goes straight up with its rms speed at $0^{\circ }\text{C}$ from the surface of the earth and there are no collision with other molecules, then it will rise to an approximate height of :

(Take $g=10m/s^2$)

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two non-zero vectors, then the value of $(\overrightarrow{A}\times \overrightarrow{B})\times (\overrightarrow{A}-\overrightarrow{B})$ is

A boy and a block, both of same mass $m\text{kg}$, are initially at the same horizontal level and attached to a frictionless pulley through a light inextensible string that moves over the frictionless pulley as shown in figure. The boy starts moving upward with an acceleration of $2.5{\text{m/s}}^2$ relative to the rope. If the block has to travel a total distance of $10\text{m}$ before reaching at the level of pulley, the time taken by the block in doing so is equal to

A projectile of mass $3m$ is projected from the ground with a velocity $30\text{m/s}$ at ${45}^{\circ }$ with the horizontal. At the highest point, it explodes into two pieces. One of pieces has mass $2m$ and the other has mass $m$. Both the pieces fly off after explosion. Mass $2m$ falls at a distance of $100\text{m}$ from the point of projection. Find the distance of second mass from the point of projection, where it strikes the ground. (Take $g=10{\text{m/s}}^2$)

The average velocity of a body moving with uniform acceleration travelling a distance $3.06\text{m}$ is $0.34\text{m/s}$. If the change in velocity of the body is $0.18\text{m/s}$ during this time, its uniform acceleration is

If the coefficient of friction between $A$ and $B$ is $\mu$, the maximum acceleration of the wedge $A$ for which $B$ remains at rest with respect to the wedge is

A metal bar with a length of 1.50 m has density 6400 $\frac{kg}{m^3}$.Longitudinal sound waves take $3.90\times {10}^{-4}$ s to travel from one end of the bar to the other. What is Young's modulus for this metal?

A man of mass $M=50\text{kg}$ stands at one end of a boat (of length $L$) which is floating in still water. The man walks to the other end of the boat. Length of the boat is $L=10\text{m}$ and mass $M=20\text{kg}$. Then the distance moved by the boat relative to the ground is

The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

Find the ratio of radius of gyration about natural axis of a circular disk to that of a circular ring each having same mass and same radius.

A $\text{SHM}$ is represented by the equation $x=10\text{sin}(\pi t+\frac{\pi }{6})$ in SI units. Find the maximum velocity of particle executing $\text{SHM}$.

A proton is released from position near to positive plate. It reaches to opposite plate in time $t_1$, now one $\alpha$ particle is released & it reaches to opposite plate in time $t_2$, then $t_1:t_2$

What is the phase difference between $I$ and $E$ if $E=E_0\sin \left(\omega t\right)$ and $I=I_0\cos (\omega t+\frac{\pi }{3})$?

A block of mass $m$ is at rest with respect to a rough inclined plane kept in an elevator moving up with an acceleration $‘a^{\prime }$. Which of the following statements is correct?

Two sheets of thickness $d$ and $3d$, are in contact with each other. The temperature just outside the thinner sheet is $T_1$ and thicker sheet is $T_3$ as shown in figure. The temperature $T_1,T_2$ and $T_3$ are in arithmetic progression such that $T_1>T_3$. The ratio of thermal conductivity of thinner sheet to thicker sheet is

Two stones $A$ and $B$ are projected from the same point. $B$ is thrown $1$ second after $A$ is thrown. $A$ is projected with a velocity of $60m/s$ at an angle ${30}^{\circ }$ with the horizontal and $B$ is projected with velocity $u$ at an angle of ${45}^{\circ }$ with the horizontal. Find $u$ if both stones hit the ground at the same time. (Take $g=10m/s$)

Planck's constant ($h$), speed of light in vacuum ($c$) and Newton's gravitational constant ($G$) are three fundamental constants. Which of the following combinations of these has the dimension of length?

One mole of $O_2$ gas having a volume equal to $22.4$ litres at $0^{\circ }C$ and 1 atmospheric pressure is compressed isothermally so that its volume reduces to $11.2$ litres. The work done in this process is

A block of mass $5\text{kg}$ slides down on a rough inclined plane of coefficient of friction $0.75$ having angle of inclination ${37}^{\circ }$ as shown in the figure. Initially if the block is at rest on the top of inclined plane of length $2\text{m}$, then the work done against the friction in moving the block to the bottom of inclined plane is (Take $g=10{\text{m/s}}^2$).

A curve is represented by y=sin x. If x is changed from $\frac{\pi }{3}to\frac{\pi }{3}+\frac{\pi }{100}$, find approximately the change in y.

The components of force $F$ parallel and perpendicular to the incline are

The orbital velocity of a satellite at point $B$ with radius $r_B$ is $v$. The radius of point $A$ is $r_A$.When satellite is at $A$, the orbit is increased in radial distances uniformly, so that $r_A$ becomes $1.2r_A$ , find the orbital velocity at $\left(1.2r_A\right)$

A block with a mass of $3\text{kg}$ is suspended from an ideal spring having negligible mass which stretches the spring by $0.2\text{m}$ at equilibrium. Find the force constant of the spring.

Which of the following is the correct result if we add the given vectors?

If the temperature of a black body increases from $7^{\circ }C$ to ${287}^{\circ }C$, the rate of energy radiation increases by

A cylinder of radius $R$ made of material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $3R$ made of a material of thermal conductivity $K_2$. The two ends of a combined systems are maintained at two different temperatures. What is the thermal conductivity of the system?

A body of mass $2\text{kg}$ is moving with constant velocity $10\text{m/s}$ on a straight line $3x+4y+5=0$. Calculate its angular momentum with respect to origin.

A solid hemisphere of radius $R$ is placed on an inclined plane of inclination $\theta .$ What will be the maximum value of $\theta$ for which the hemisphere will not topple? (Assume that the solid hemisphere will not slide)

The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is ($g=10m/s^{-2}$)

So in 2D motion does the instantaneous acceleration always have to be along the same line as velocity( either 0 or 180 degrees)?

The given setup is in equilibrium springs were in natural length before force was applied. If I have to replace the above setup of 1 block and 2 springs by 1 block and 1 spring, What will be the spring constant of that new spring, such that the block is displaced by the same amount as previously.

A steel rod of length $5\text{m}$ and diameter $30\text{mm}$ is fixed between two rigid supports. Determine the thermal stress and change in diameter of the rod, when the temperature increases by $50{}^{\circ }\text{C}$. Take Young's modulus of elasticity $\left(Y\right)=2.0\times {10}^6{\text{kg/cm}}^2$, coefficient of thermal expansion $\left(\alpha \right)=12\times {10}^{-6}{/}^{\circ }\text{C}$ and Poisson's ratio $\left(\nu \right)=0.3$.

A particle is suspended by thread of length $l$ from a fixed point. If it is launched from the bottom with a horizontal speed of $v=\sqrt{5gl}$, then tension in the thread when the particle is at the topmost point

In a thermodynamic process, pressure of a fixed mass of gas is changed in such a manner that the gas releases $20\text{J}$ of heat and $8\text{J}$ of work is done on the gas. If initial internal energy of the gas was $30\text{J}$, then the final internal energy will be

Calculate the change in intensity level when the intensity of sound increases by ${10}^6$ times its original intensity.

A liquid of density $\rho$ and surface tension $\sigma$ rises to a height $h$ in a capillary tube of diameter $d$. The weight of the liquid in the capillary tube is:

(Consider liquid to be perfectly wetting in nature.)

The potential difference ($V_A–V_B$) between the points A and B in the given figure is