Explore topic-wise InterviewSolutions in .

A small mass starts sliding down a fixed inclined plane of inclination ${45}^{\circ }$ with the horizontal. The coefficient of friction is $\mu ={\mu }_{0}x$ where $x$ is the distance through which the mass slides down and ${\mu }_0$ is a constant. Find the heat produced during half the distance travelled by the particle before it stops.

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

A flatcar having mass $m_0=50\text{kg}$, is moving to the right due to a constant horizontal force $F=20\text{N}$. Raindrops fall perpendicularly on the flatcar at a constant rate equal to $\mu =10\text{kg/s}$. Find the acceleration of the flatcar (at $t=10\text{sec}$). Assume friction is negligibly small.

A liquid is under streamline flow through a horizontal pipe of non uniform cross-sectional area. If the volume rate of flow at a cross-section of area $a$ is $V$, then volume rate of flow at a different cross-section of area $\frac{a}{2}$ is

Percentage change in moment of inertia of a solid body when temperature is changed by ${50}^{\circ }\text{C}$ is

$[{\alpha }_{\text{body}}=12\times {10}^{-6}{/}^{\circ }\text{C}]$

A person $AB$ of height $170\text{cm}$ is standing in front of a plane mirror. His eyes are at height $164\text{cm}$. At what distance from $P$ should a hole be made in the mirror so that he cannot see his hairs?

A car moving with a speed of $50\text{km/h}$ can be stopped by brakes after at least $6\text{m}$. If the same car is moving at a speed of $100\text{km/h}$, the minimum stopping distance is:

The frequency of the first line in Lyman series in the hydrogen spectrum is $v$. What is the frequency of the corresponding line in the spectrum of doubly ionized Lithium?

The separation $L$ between the objective $(f=0.5cm)$ and the eyepiece $(f=5cm)$ of a compound microscope is $7cm$.



If a small object be placed so that the eye is least strained to see the image, find the angular magnification produced by the microscope.

Integrate the following w.r.t $x:\frac{1}{2x+3}$

An ant moves from A to B then to c, what is the distance (d) and displacement (s) of the ant?

A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction $\mu$. It is compressed by a distance a from its normal length and, on being released, it moves to a distance $b$ from its equilibrium position. The decrease in amplitude for one half-cycle $(-atob)$ is

A uniform chain of length l is placed on the table in such a manner that its l' part is hanging over the edge of table without the chain sliding. If the coefficient of friction between the chain and the table is $\mu$ then find the maximum length of chain l' that can hang without the entire chain slipping.

An open knife edge of mass 'm' is dropped from a height 'h' on a wooden

floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is

Current in the circuit will be

Two moles of helium $\left(He\right)$ are mixed with four moles of hydrogen $\left(H_2\right)$. The value of $\gamma$ of the mixture is

A force F is acting on a body and its component along x-axis is 60 N. The Force F is inclined at an angle ${30}^{\circ }$ as shown. Determine F.

At $t=0$ a projectile is fired from a point $\text{O}$ (taken as origin) on the ground with a speed of $50m/$s at an angle of ${53}^{\circ }$ with the horizontal. It just passes two points $A$ and $B$ each at height $75m$ above the horizontal as shown.



The horizontal separation between the points $A$ and $B$ is

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

Two small balls A and B, each of mass m, are attached rigidly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed $\omega$. The angular momentum of the system about the axis of rotation is .

Three boys are standing on a horizontal paltform of mass $170\text{kg}$ and length $6\text{m}$ is as shown in figure. They exchange their position as shown in the figure. Distance moved by the platform is : (Neglect friction)

A man runs towards a mirror at a speed $+6\text{m/s}$. If the mirror is at rest, his image will have a velocity (with respect to man)

A tube has two areas of cross-section as shown in the figure. The diameter of the bigger section is double the diameter of the smaller section. Find the range of water falling on the horizontal surface, if piston is moving with a constant velocity $0.4\text{m/s}$ and $h=2.5\text{m}(g=10{\text{m/s}}^2)$

Find the electric field at the symmetric centre. There is no charge at point P.

Find the least pulling force acting at an angle of ${30}^{\circ }$ with the horizontal, which can just slide a body of mass $10\text{kg}$ along a rough horizontal surface $[{\mu }_s={\mu }_k=\frac{1}{\sqrt{3}},g=10m/s^2]$

Water from a tap emerges vertically downwards with initial velocity $4{\text{ms}}^{-1}$. The cross-sectional area of the tap is $A$. The flow is steady and pressure is constant throughout the stream of water. The distance $h$ vertically below the tap, where the cross-sectional area of the stream becomes $\frac{2}{3}A$, is:

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

A fixed wedge with both surfaces inclined at ${45}^{\circ }$ to the horizontal is shown in the figure. A block $P$ of mass $m$ is held on the smooth plane by a light string which passes over a smooth pulley A and is attached to a block $Q$ of mass $3m$ which rests on the rough plane. The system is released from rest. Given that the acceleration of each block is of magnitude $\frac{g}{5\sqrt{2}}$ then, the tension in the string is

For an ideal gas the fractional change in its volume per degree rise in temperature at constant pressure is equal to

$[T$ is the absolute temperature of gas $]$

Rays from a lens are converging toward a point $P$ as shown in figure. How much thick glass plate having refractive index $1.6$ must be located between the lens and point $P$, so that the image will be formed at $P$’?

The angular velocity of a particle rotating in a circular orbit 100 times per minute is

The momentum of a photon of energy hv will be

Two small rings, each of mass ${}^{\prime }{m}^{\prime }$, are connected to the block of same mass ${}^{\prime }{m}^{\prime }$ through an inextensible massless string of length ${}^{\prime }{l}^{\prime }$. Rings are constrained to move over smooth rod $AB$. Initially, the system is held at rest as shown in Figure. Let $u$ and $v$ be the velocities of ring and block, respectively when string makes an angle ${60}^{\circ }$ with the vertical.

Dimensional homogeneity for an equation is ___

A plane mirror hinged at O is free to rotate in a vertical plane. The point O is at a distance x from a long screen placed in front of the mirror as shown in figure. A laser beam of light incident vertically downward is reflected by he mirror at O so that a bright spot is formed at the screen.

At the instant shown, the angle of inclidence is $\theta$ and the mirror is rotating clockwise with constant angular velocity w. Find the speed of the spot at this instant.

A stone is projected from the ground with velocity 25 m/s. Two seconds later, it just clears a wall 5 m high. The angle of projection of the stone is $(g=10m/se{c}^2)$

On a cold winter day, the atmospheric temperature is $-\theta$ (on Celsius scale) which is below $0^{\circ }\text{C}$. A cylindrical drum of height $h$ made of a bad conductor is completely filled with water at $0^{\circ }\text{C}$ and is kept outside without any lid. Calculate the time taken for the whole mass of water to freeze. Thermal conductivity of ice is $K$ and its latent heat of fusion is $L$. Neglect expansion of water on freezing.

In P-type semiconductor, there is

If force $\left(F\right)$, velocity $\left(V\right)$ and time $\left(T\right)$ are taken as fundamental units, then dimensions of mass are

With respect to a rectangular cartesian co-ordinate system three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and $\overrightarrow{c}=-\hat{k}$ where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along the x, y, z axes respectively. The unit vector along the direction of sum of these vectors is

A block of mass $m$ is moving with an initial velocity $v_0$ towards a stationary spring of stiffness $k$ attached to the wall as shown. Find the maximum compression in the spring.

A point object $O$ is placed in front of a plane mirror as shown in the figure. In order to see the image in mirror, the region where a person must place his eyes is best represented as:

A Carnot engine operates at an efficiency of $40\%$ with the sink at ${27}^{\circ }C$. Find the amount by which the temperature of the source must be increased in order to increase the efficiency by $10\%$.

A load of 4.0 kg is suspended from a ceiling through a steel wire of length 20 m and radius 2.0 mm. It is found that the length of the wire increases by 0.031 mm as equilibrium is achieved. Find Young modulus of steel. Take $g=3.1\pi m{s}^{-2}.$

Two containers of equal volume contain the same gas at different pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$, respectively. On joining the vessels, the gas reaches a common pressure $P$ and common temperature $T$. The ratio $\frac{P}{T}$ is equal to

If a spring extends by $x$ on loading, then energy stored by the spring is (Given: $T$ is the tension in spring and $k$ is spring constant)

A block is projected along a rough horizontal surface with a velocity of $5\text{m/s}$. If the block comes to rest after travelling a distance of $4\text{m}$, then the coefficient of kinetic friction is $(\text{Take}g=10{\text{m/s}}^2)$

Potential energy of a particle along $x-$ axis is given by $U=[-20+(x-2{)}^2]\text{J}$. Force on the particle at $x=0$ is

A bus starts moving with acceleration $2{\text{ms}}^{-2}$. A cyclist $96\text{m}$ behind the bus starts simultaneously towards the bus at a constant speed of $20\text{m/s}$. After what minimum time will he be able to overtake the bus?

A hall has the dimensions $10m\times 10m\times 10m.$ A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its displacement is nearly

A small sphere of density $\rho$ falls from rest into a viscous liquid of density $\sigma$ and viscosity $\eta$. Due to friction, heat is produced. Which of the follwing options correctly represents the relation between the rate of production of heat $H$ and the radius of the sphere $r$ at terminal velocity?

A block of mass $1kg$ lies on horizontal surface in a truck. The coefficient of static friction between the block and the surface is ${\mu }_s=0.6$. If the acceleration of the truck is $5m/s^2$, the friction force acting on the block is