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A block is placed on an inclined plane moving horizontally towards right with an acceleration $a=g$. Take $g=10{\text{ms}}^{-2}$ .The length of plane $\text{AC}=1\text{m}$. Friction is absent everywhere. Time taken by the block to reach from $\text{C}$ to $\text{A}$ is

For the circuit shown in below figure, current in the inductor is $0.8\text{A}$ while in the capacitor is $0.6\text{A}$. What is the current drawn from the source?

In the figure shown below, two particles have masses $2\text{kg}$ each and they are moving with velocities $4\text{m/s}$ and $2\text{m/s}$ respectively towards each other. Assume the collision between the particles is perfectly elastic. Find their respective magnitudes of velocities after the collision.

A particle is projected with a velocity $u$ at two different angles which are complementary to each other. If $H_1$ and $H_2$ are the heights attained by them in each case, find the range of the particle.

The capacitance of the capacitor of plate areas $A_1$ and $A_1$at a distance d, as

shown in the figure, is:

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half – submerged state. If ${\rho }_c$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

A plank is moving with a velocity $4\text{m/s}$. A disc of radius $1\text{m}$ rolls on it without slipping with an angular velocity of $3\text{rad/s}$ as shown in figure. Then, the velocity of the centre of the disc $\left(V_{\text{cm}}\right)$ is

Find the displacement of the wedge when the mass 'm' has comes out of the wedge. There is no friction anywhere.

A metal ball of mass $1.0\text{kg}$ is kept in a room at ${15}^{\circ }\text{C}$. It is heated using a heater. The heater supplies heat to the ball at a constant rate of $24\text{W}$. The temperature of the ball rises as shown in the graph. Assuming that Newton's law of cooling can be used, calculate the rate of heat loss from the ball when it is at a temperature of ${20}^{\circ }\text{C}$.

A wheel having moment of inertia $I=4{\text{kg-m}}^2$ about its natural axis is rotating at the rate of ${\omega }_o=120\text{rpm}$. Find the magnitude of constant torque which can stop the wheel in $3$ minutes.

Find the projection of $(\overrightarrow{a}+2\overrightarrow{b})$ on $\overrightarrow{c}$ where $\overrightarrow{a}=2\hat{i}-2\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}+2\hat{j}-2\hat{k}$ and $\overrightarrow{c}=2\hat{i}-\hat{j}+4\hat{k}$

Photo cell is a device to

An insect wants to go from one corner of cube to diagonaly opposite corner by crawling [can't fly]. Minimum distance it has to travel to reach there if side of cube is a

A particle of mass $3\text{kg}$ moving with a velocity of $6\hat{i}\text{m/s}$ collides head on with another particle of mass $5\text{kg}$ moving with a velocity of $-2\hat{i}\text{m/s}$. If after the collision, first particle has a speed of $1\text{m/s}$ along the negative $X$ axis, find the coefficient of restitution.

A road is $7.5\text{m}$ wide and its outer edge is raised by $1.5\text{m}$ over the inner edge. The radius of curvature is $50\text{m}$. If $g=10{\text{m/s}}^2$, for what speed of the car is this road suited?

A conducting rod of length $l$ falls vertically under gravity in a region of uniform magnetic field $B$. The field vectors are inclined at an angle $\theta$ with the horizontal as shown in figure. If the instantaneous velocity of the rod is $v$, the induced emf in the rod $ab$ is

A ball of mass $1\text{kg}$ is thrown with a velocity of $6\text{m/s}$ at a stone of unknown mass initially at rest. If the velocity of the stone after the elastic collision with the ball is $1.5\text{m/s}$, what is the mass of the stone?

If $y=x^2+2x-3$, y-x graph is

In anomalous expansion of water, at what temperature the density water is maximum?

Given that $0.2\hat{i}+0.6\hat{j}+a\hat{k}$ is a unit vector. What is the value of a?

A and B are two metallic pieces. They are fully immersed in water and then weighed. Now they show same loss of weight. The conclusion therefore is:

A body is projected vertically upward with speed $40m/s$. The distance travelled by the body in last 2 second of the journey is $[g=10m/s^2]$

A square wire frame of size $L$ is dipped in a liquid. On taking out, a membrane is formed. If the surface tension of liquid is $T$, then force acting on a frame will be

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of water in the capillary tube is $5\text{g}$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is:

Find the friction force between block $A$ and the surface for system at rest given below:

$m_A=9\text{kg},m_B=4\text{kg},{\mu }_s={\mu }_k=0.8$

A coil of inductance L is carrying a steady current i. What is the nature of its stored energy?

A man is standing in a valley between two parallel mountains. He fires a gun and hears echo at an interval of 2s and 3.5s. what is the distance between 2 mountains? (Take speed of sound = 350 m/s)

A brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to that of the carbon disc is

[${\alpha }_B$ and ${\alpha }_C$ are respectively the temperature coefficients of resistance of brass and carbon & ${\rho }_B$ and ${\rho }_C$ are respectively the resistivities of brass and carbon. Neglect linear expansion]

In a YDSE, light of wavelength $\lambda =5000\stackrel{\circ }{A}$ is used, which emerges in phase from two slits a distance $d=3\times {10}^{-7}m$ apart. A transparent sheet of thickness $t=1.5\times {10}^{-7}m$, refractive index $n=1.17$, is placed over one of the slits. Where does the central maxima of the interference now appear from the center of the screen? (Find the value of y?)

In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a U-tube connected to the gas at one end. When the bulb is placed at the room temperature 27.0℃, the mercury column in the arm open to atmosphere stands 5.00 cms above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0 cms. Calculate the temperature of the liquid. (Atmospheric pressure = 75.0 cm of mercury.)

In the figure shown, all the blocks are of equal mass of $10\text{kg}$ and $F=300\text{N}$. Find the tension in the string, $T_{BC}$. Assume all surface to be smooth and $g=10{\text{m/s}}^2$.

In the figure shown, if the velocity of end A is $v_0$, find the velocity of the end $B$ of the rigid rod at the given instant.

A man $(\text{mass}=50\text{kg})$ and his son $(\text{mass}=20\text{kg})$ are standing on a frictionless surface facing each other. The man pushes his son, so that he starts moving at a speed of $0.70{\text{ms}}^{-1}$ with respect to the man. The speed of the man with respect to the surface is

Two miscible fluids of densities 1.2 gm/cm³ and 1.4 gm/cm³ are mixed with a proportion of their volumes equal to 3:5. Assuming both fluids to be perfectly miscible, what is the density of resulting liquid?

In the given figure, what maximum force F can be applied on wedge of mass M, so that block of mass m does not move with respect to wedge.

A man is rowing a boat with a constant velocity $v_o$ in a river of depth ${}^{\prime }{D}^{\prime }$. The contact area of boat is ${}^{\prime }{A}^{\prime }$ and coefficient of viscosity of water is $\eta$. Find the force required to row the boat.

A wooden bowl conducts less heat than a copper bowl because

What should be the acceleration ${}^{\prime }{a}^{\prime }$ of the box shown in figure so that the block of mass $m$ exerts a force $\frac{mg}{4}$ on the floor of the box ? (where $g$ is acceleration due to gravity)

The earth $(mass=6\times {10}^{24}kg)$ revolves round the sun with angular velocity $2\times {10}^{-7}rad/s$ in a circular orbit of radius $1.5\times {10}^{8}km$. The force exerted by the sun on the earth in newtons, is

A block of mass $10\text{kg}$ is placed on rough horizontal surface whose coefficient of friction is $0.5$. If a horizontal force of $100\text{N}$ is applied on it along the surface , then acceleration of block will be [Take $g=10{\text{ms}}^{-2}$]

Find the electric at a point O.

A body of mass $m$ moving with a speed $v$ suffers an inelastic collision with another body of mass $M=2m$ at rest. The speed of the composite body will be

The distance between two particles is decreasing at the rate of $6\frac{m}{sec}$. If these particles travel with same speeds as in previous case and in the same direction, then the separation increase at the rate of $4\frac{m}{sec}$. The particles have speeds as

A car is moving in a circular horizontal track of radius $10\text{m}$ with a constant speed of $10\text{m/s}$. A bob is suspended from the roof of the car by a light wire of length $1\text{m}$. The angle made by the wire with the vertical is

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

A smooth semicircular wire track of radius $R$ is fixed in a vertical plane as shown in the figure. One end of a massless spring of natural length $\frac{3}{4}R$ is attached to the lowest point $O$ of the wire track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The spring makes an angle of ${60}^0$ with the vertical. The spring constant is $k=\frac{mg}{R}$. Consider the instant when the ring is making an angle of ${60}^0$ with the vertical. Find the tangential acceleration of the ring.

A projectile is given an initial velocity of $(2\hat{i}+4\hat{j})$$m/s$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g=10m/s^2$, then the equation of its trajectory is

A particle is dropped from a height $h=100\text{m}$, from the surface of a planet. If in the last $\frac{1}{2}\text{sec}$ of its journey, it covers $19\text{m}$, the value of acceleration due to gravity on that planet is:

The angle of incidence at which, reflected ray is totally polarised for reflection from air to glass (refractive index $=n$) is: