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A refrigerator door is $150\text{cm}$ high, $80\text{cm}$ wide and $6\text{cm}$ thick. If the coefficient of conductivity is $0.0005{\text{cal/cm-s-}}^{\circ }\text{C}$ and the inner and outer surfaces are at $0^{\circ }\text{C}$ and ${30}^{\circ }\text{C}$ respectively, find the heat loss per minute through the door. (in Calories)

Two point charges placed at a distance ${}^{\prime }{r}^{\prime }$ in air exert a force ${}^{\prime }{F}^{\prime }$. The distance at which they exert same force when placed in a certain medium (dielectric constant $K$) is

A block of mass m is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally, so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be:

A metal rod of length $50\text{cm}$ having mass $2\text{kg}$ is supported on two edges placed $10\text{cm}$ from each end. A $3\text{kg}$ load is suspended at $20\text{cm}$ from one end. Find the reactions at the edges (take $g=10{\text{m/s}}^2$)

Let $x_0,y_0$ be fixed real numbers such that $x_0^2+y_0^2>1$. If $x,y$ are arbitrary real numbers such that $x^2+y^2\le 1$, then the minimum value of $(x–x_0{)}^2+(y–y_0{)}^2$ is

Is Lambda one is the wavelength of the photon emitted by the electron when it jumps from third Orbit to first Orbit and Lambda 2 is the wavelength of the photon emitted by the electron when it jumps from third Orbit to second orbit and Lambda 3 is the wavelength of the photon emitted by the electron when it jumps from orbit second to orbit first derive a relation between Lambda 1 Lambda 2 and Lambda 3

Two equal drops of water are falling through air with a steady velocity $v$. If the drops coalesce, the new velocity will be

An aircraft executes a horizontal loop of radius $1\text{km}$ with a steady speed of $900{\text{kmh}}^{-1}$. Find its centripetal acceleration.

The pendulum hanging from the ceiling of a railway carriage makes an angle ${30}^{\circ }$ with the vertical when it is accelerating. The acceleration of the carriage is

A thin lens of focal length $f$ and its aperture diameter $d$, forms a real image of intensity $I$. Now the central part of the aperture upto diameter $\left(\frac{d}{2}\right)$ is blocked by an opaque paper. The focal length and image intensity would change to

If a square shape of side $5\text{cm}$ is cut from a square sheet of side $10\text{cm}$. Find the sum of $x$ and $y$ coordinates of the centre of mass of the remaining part as shown in the figure below. Consider the origin at the corner as shown in figure. Material is considered to be of uniform density.

A bubble having surface tension T and radius R is formed on a ring of radius b (b << R). Air is blown inside the tube with velocity v as shown. The air molecules collide perpendicularly with the wall of the bubble and stops. Calculate the radius at which the bubble separates from the ring.

A body starts from rest and travels with uniform acceleration such that it covers $8m$ during the $2^{nd}$ second. The distance it would travel during the $5^{th}$ second is

The acceleration of a particle starting from rest vary with respect to time is given by a = (2t - 6), where t is in seconds. Find the time at which velocity of particle in negative direction is maximum.

A ball falls on an inclined plane of inclination $\theta ={30}^o$ from a height $h=10\text{m}$ above the point of impact and makes a perfectly elastic collision. Find the maximum height attained by the ball, perpendicuar to wedge surface. (take $g=10{\text{m/s}}^2$)

Find the binding energy of a hydrogen atom in the state n = 2.

In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

How to calculate phase difference between the two waves?

Calculate the dimensions of force and impulse taking velocity, density and frequency as the basic quantities

What happens to a charged particle when it is accelerated along the direction of magnetic field ?

A particle circulating in a circular path has angular momentum L if its rotational kinetic energy is halved and frequency is doubled then what will be angular momentum

What is emission spectrum?

A body starts with velocity u and moves in a straight line with constant acceleration a. When it's velocity has increased to 5u, the acceleration is reversed in direction, the magnitude remains the same. Find the velocity with which the body passes the starting point again.

Why is it so that no body is rigid?

A ball of mass $10kg$ is moving with a velocity of $10m/s$. It strikes another ball of mass $5kg$, which is moving in the same direction with a velocity of $4m/s$. If the collision is elastic, their respective velocities after the collision will be

When a battery is connected across a series combination of self inductance L and resistance R, the variation in the current i with time t is best represented by

how does lighting happens

The efficiency of a Carnot heat engine is $\frac{1}{3}.$ Find the coefficient of performance of Carnot refrigerator when both heat engine and refrigerator are working between similar source and sink.

A body starts from rest and slides down the inclined surface of a smooth inclined plane having inclination $\theta$ with the horizontal. The time taken by the body to reach the bottom is

A graph between the square of velocity of a particle and the distance S moved by the particle is as shown in the figure. then the acceleration of particle is

Two blocks of masses $m_1$ and $m_2$ are connected as shown in the figure. The acceleration of the block $m_2$ is

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights, viz $a$ and $b$. The ratio of time taken by the two to drop through these distances is

The given figure shows the $v-t$ graph of a particle moving in a straight line. At time $t$ it returns to the starting point. Find $t$. (Assume SI units for the graph)

The velocity of water in a river is 18 km h^-1 near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = 10^-2 poise.

Find the second derivative of the following function: $y=e^{3x+2}$

A motor cyclist moving with a velocity of $72\text{km/h}$ on a flat frictionless road takes a turn on the road at a point where the radius of curvature of the road is $20\text{m}$. The acceleration due to gravity is $10{\text{m/s}}^2$. In order to avoid skidding, he must bend with respect to the vertical plane by an angle