Explore topic-wise InterviewSolutions in .

Two short bar magnets of magnetic moments $‘M^{\prime }$ each are arranged at the opposite corners of a square of side $‘d^{\prime }$ such that their centres coincide with the corners and their axes are parallel to one side of the square. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is.

Two blocks of masses $M_1$ and $M_2$ are connected with a string passing over a pulley as shown in the figure. The block $M_1$ lies on a horizontal surface. The coefficient of friction between the block $M_1$ and the horizontal surface is $\mu$. The system accelerates. What additional mass $m$ should be placed on the block $M_1$ so that the system does not accelerate?

A rod $AB$ is shown in figure. End $A$ of the rod is fixed on the ground. Block is moving with velocity $\sqrt{3}\text{m/s}$ towards right. The velocity of end $B$ of rod when rod makes an angle of ${60}^{\circ }$ with the ground is

A ball is thrown vertically downwards from a tower of height $60\text{m}$ with a speed of $20\text{m/s}$. The $y\text{(m)}-t$ curve of the ball is

[Take $g=10{\text{m/s}}^2$, consider point of projection as origin and upward displacement as positive]

Three particles of masses $2\text{kg},3\text{kg}$ & $4\text{kg}$ are placed at the three vertices of a right angled triangle with sides $3\text{cm},4\text{cm}$ & $5\text{cm}$ as shown in the figure. What will be the coordinates of centre of mass of the system of particles ?

A horizontal uniform rod of mass ${}^{\prime }{m}^{\prime }$ has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass ${}^{\prime }{m}^{\prime }$ which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.





The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force on the cylinder due to the inclined plane is:

In Young's double slit experiment, the distance of the $n^{th}$ dark fringe from the centre is-

A man swims with a speed of $4km/h$ in still water. The speed of the river is $3km/h$. He starts swimming in the river perpendicular to the direction of the flow of the current of the river. The river is $2km$ wide. What is the horizontal shift of the man?

With what acceleration ${}^{\prime }{a}^{\prime }$ shown, the elevator descends so that the block of mass $M$ exerts a force of $\frac{Mg}{10}$ on the weighing machine? [$g$ = acceleration due to gravity]

Two moles of helium $\left(He\right)$ are mixed with four moles of hydrogen $\left(H_2\right)$. The molar heat capacity of the mixture at constant pressure is

If the radius of earth contracts $\frac{1}{n}$ of its present value, the length of the day will be approximately

A ring of mass m and radius R and a sphere of mass M and same radius R are separated by a distance $\sqrt{8}R$ as shown in the figure. The force of attraction between the ring and the sphere is

A wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross - sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$ and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is-

Two pulley arrangements of figure given are identical. The mass of the rope is negligible. In fig (a), the mass $m$ is lifted by attaching a mass $2\text{m}$ to the other end of the rope. In fig (b), $m$ is lifted up by pulling the other end of the rope with a constant downward force $F=2mg$. The acceleration of $m$ in the two cases are respectively

The displacement of a particle varies with time $t$ as: $s=\alpha t-\beta t^2$. Determine the time $\left(t\right)$ at which velocity of the particle becomes $0$.

A gas mixture contains $1\text{g}{H}_2$ and $1\text{g He}$. If temperature of gas mixture is increased from $0^{\circ }C$ to ${100}^{\circ }C$ at isobaric process, then find the heat given to the gas mixture. $[{\gamma }_{He}=\frac{5}{3},{\gamma }_{He}=\frac{7}{5},R=2\text{cal/mol-K}]$

A block of weight $10N$ is fastened to one end of a wire of cross-sectional area $3m{m}^2$ and is rotated in a vertical circle of radius $20cm$. The speed of the block at the bottom of the circle is $2m{s}^{-1}$. If the Young modulus of the material of the wire is $2\times {10}^{11}N{m}^{-2}$, what is the elongation of the wire when the block is at the bottom of the circle?

Both springs, string and pulley shown in the figure are light. Initially when both the springs were in their natural state, the system was released from rest. The maximum displacement of the block having mass $m$ is:

A point source of light $B$ is placed at a distance $L$ in front of the center of a mirror of width $d$ hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance $2L$ from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

Two bodies move towards each other from 10 m apart with a constant velocity they meet at C after 2s. What is the displacement of B w.r.t. A?

The resultant of two forces having magnitude $8\text{N}$ and $15\text{N}$ is $17\text{N}$. Find the angle between forces of $8\text{N}$ and $15\text{N}$.

At the height 80 m, an aeroplane is moving with 150 m/s. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped (given g = 10 $m/s^2$)

According to De Broglie the electron in n=3 of $L{i}^{++}$ atom will look like

The equation of a particle executing SHM is $y=20\sin (2\pi t-\frac{\pi }{3})$.

The amplitude $A$, time period $T$ and angular frequency $\omega$ are

[All quantities are in SI units]

Which of the given vector is a negative vector?

The frequency of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of the tuning fork $C$. When $A$ and $B$ are simultaneously excited then $5$ beats per second are produced. The frequency of the tuning fork $A$ is

The pulley shown in figure has moment of inertia $I=5{\text{kg-m}}^2$ about its axis and radius $R=1\text{m}$. Find the acceleration of the blocks if the masses of the blocks are $M=3\text{kg}$ and $m=2\text{kg}$. Assume that the string is light and does not slip on the pulley and $g=10{\text{m/s}}^2$.

When is the object at rest?

A $150\text{g}$ block oscillates in SHM on the end of a spring with $k=1500\text{N/m}$, according to the relation $x=x_0\cos (\omega t+\varphi ).$ How long does the block take to move from the position $+0.800x_0$ to $+0.600x_0$ directly ?

An old man and a boy are walking towards each other and a bird is flying over them as shown in the figure.

Find the velocity of tree, bird and old man as seen by boy respectively.

A flatcar of mass $m_0=20\text{kg}$ is moving to the right due to a constant horizontal force $F=10\text{N}$. Sand spills on the flatcar from a stationary hopper. The velocity of loading is constant and equal to $\mu =1\text{kg/s}$.







Find the acceleration of the flatcar after $t=20\text{s}$.

A particle executes SHM with a period of $T$ second and amplitude $A$ metre. The particle is at its mean position initially. The shortest time it takes to reach point $\frac{A}{\sqrt{2}}$ metre from its mean position in seconds is

A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of 60${}^{\circ }$ and then released. Find the magnitude of the force acting on a particle of mass 'dm' at the tip of the rod, when rod makes an angle of 37${}^{\circ }$ with the vertical.

Which one of the following graph represents the behaviour of a ideal gas? Assume pressure is constant.

Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side 'd' at t = 0. Each of the particles moves with constant speed v. A always has its velocity along AB, B along BC and C along CA. At what time will the particles meet each other?

Figure shows a spring fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $5.8\text{m}$ away from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. The friction coefficient between the plane and the block and the spring constant of the spring is (Take $g=10{\text{m/s}}^2$)

In a sample of an ideal gas the average momentum of a molecule depends on

In a radioactive decay chain, ​${}_{90}^{232}Th$ nucleus decays to ${}_{82}^{212}Pb$ nucleus. Let $N_{\alpha }$ ​ and $N_{\beta }$ ​ be the number of α and ${\beta }^{-}$ particles respectively, emitted in this decay process. Which of the following statements is (are) true?

A $2\text{kg}$ block slides on a horizontal floor with a speed of $4\text{m/s}$. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is $15\text{N}$ and spring constant is $10,000\text{N/m}$. The spring compresses by

An asteroid is going to hit the Earth. To calculate its distance it is observed from 2 diametrically opposite points A, B on Earth. The angle subtended at the asteroid by these two directions of observations is $2^o$. Given the diameter of Earth to be about $1.276\times {10}^7$ m. compute the distance of the asteroid.

A car is going at a speed of $6\text{m/s}$ when it encounters a $15\text{m}$ slope of angle ${30}^{\circ }$. The friction coefficient between the road and the tyre is $0.5$. The driver applies the brakes.

The minimum speed of the car with which it can reach the bottom is around $(g=10{\text{m/s}}^2)$

The maximum speed of a car on a road–turn of radius 30 m, if the coefficient of friction between the tyres and the road is 0.4, will be

The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from :

Figure shows an imaginary cube of side $a$. A uniformly charged rod of length $a$ moves towards right at a constant speed $v$. At $t=0$, the right end of the rod just touches the left face of the cube. Which of the following represents the correct graph between electric flux passing through the cube with time?

A man is pulling a block resting on the ground by applying force $F=(20t+40)\text{N}$ as shown in the figure. If the pulley is frictionless and mass of the block is $4\text{kg}$, find out the power delivered by the force, $3\text{seconds}$ after the man starts pulling the block. (Take $g=10{\text{m/s}}^2$)

Eight small drops of equal size are falling through air with a steady velocity of $10\text{cm/sec}$. If the drops coalesce, what would be the terminal velocity of the bigger drop?

The frequency of a radar is 780 MHz. After getting reflected from an approaching aeroplane, the apparent frequency is more than the actual frequency by 2.6 kHz. The aeroplane has a speed of