Explore topic-wise InterviewSolutions in .

What should be the maximum speed with which a car can be driven through a curve of radius $18m$ without skidding (where, $g=10m{s}^{-2}$, coefficient of static friction between the rubber tyres and the roadway is $0.2$)?

The side of a cube is measured by vernier caliper ($10$ divisions of vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1\text{mm}$). The main scale reads $10\text{mm}$ and the first division of the vernier scale coincides with the main scale. The maximum $\%$ error in measurement of volume of the cube will be

A car is moving on a circular level road of radius of curvature $300\text{m}$. If the coefficient of friction is $0.5$ and taking $g=10{\text{m/s}}^2$, the maximum speed the car can have (in $\text{km/hr}$) is

A spherical body radiates $300\text{W}$ power at $650\text{K}$. If the radius were halved and temperature doubled, then find the power radiated.

As shown in the figure a ball of mass $m$ hits a floor with a speed $u=10\sqrt{2}\text{m/s}$ making an angle of incidence $\alpha ={45}^{\circ }$ with the normal. The coefficient of restitution is $e=0.5$. Find the speed of the reflected ball and the angle of the reflection.

A particle of mass $m$ is moving with speed $2v$ and collides with a mass $2\text{m}$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle ${45}^{\circ }$ with respect to the original direction.

The speed of each of the moving particle will be

A certain string (fixed at one end and free at the other end) can vibrate at several frequencies, the lowest of which is $200\text{Hz}$. What are next two higher frequencies to which it vibrates?

A ball is thrown from ground level of a field with a speed of 12.0 m/s at an angle of ${45}^{\circ }$ with the horizontal. At what distance will it hit the field again? Take g = 10.0 m/$s^2$.

An eye specialist prescribes spectacles having combination of convex lens of focal length $40\text{cm}$ in contact with a concave lens of focal length $25\text{cm}$. The power of this lens combination in diopters is

Two vibrating strings are of same material but lengths l, 2l and radii 2r, r respectively are stretched under the same tension. Both are vibrating in their fundamental modes. The experimental arrangement is such that first string has both ends fixed, second string vibrates with one end fixed and other end as free.

If the frequencies of vibration of first and second wire are $n_1$ and $n_2$, then $\frac{n_1}{n_2}$= ________

Find the electrostatic energy stored in a cylindrical shell of length $l$, inner radius $a$ and outer radius $b$, coaxial with a uniformly charged wire with linear charge density $\lambda$.

A uniform rectangular lamina $\text{ABCD}$ is of mass $M$, length $a$ and breadth $b$, as shown in the figure. If the shaded portion $\text{HBGO}$ is cut-off, the coordinates of the centre of mass of the remaining portion will be

A layer of ice at $0^{\circ }\text{C}$ of thickness $x_1$ is floating on a surface of water. $L,\rho$ and $K$ respectively are the latent heat of fusion of ice, density of ice and thermal conductivity of ice. If the atmospheric temperature is $-T^{\circ }\text{C}$, the time taken for the thickeness of the layer of ice to increase from $x_1$ to $x_2$ is given by

A particle executes a SHM with frequency $\nu$. The frequency of variation of potential energy will be :

In the figure shown below, a quarter ring of radius $r$ is placed in the first quadrant of a cartesian co-ordinate system, with centre at origin. Find the co-ordinates of $COM$ of the quarter ring.

A physical quantity of the dimensions of length that can be formed out of $c,G\text{and}\frac{e^2}{4\pi {ϵ}_0}$ is [$c$ is velocity of light, $G$ is universal constant of gravitation and $e$ is charge] :

The velocity of light in air is $3\times {10}^8$ m/s and in a medium is $\sqrt{3}\times {10}^8$ m/s. The Brewster’s angle of the medium is

Using the concept of significant figures, match Column I with the correct number of significant figures in Column II.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ i& 0.1234& \text{a.}& 5\\ ii& 1.2100\text{cm}& \text{b.}& 4\\ iii& 47.23÷2.3& \text{c.}& 1\\ iv& 3\times {10}^8& \text{d.}& 2\end{array}$

A biker is moving with a speed of $15\text{m/s}$ on a flat road. The coefficient of friction between the wheels of the bike and the road is $0.4$. If he approaches a curve, what is the minimum radius of the turn that he can take safely?

50 g of copper is heated to increase its temperature by ${10}^{\circ }C.$ If the same quantity of heat is given to 10 g of water, the rise in its temperature is:

Specific heat of copper is $420Jk{g}^{-1}{}^{\circ }C$.

The speed of a transverse wave, travelling on a wire having a length of $100\text{cm}$ and mass $10\text{g}$ is $160\text{m/s}$. The area of cross-section of the wire is $2{\text{mm}}^2$ and its Young's modulus is $32\times {10}^{11}{\text{N/m}}^2$. Find the extension of the wire from its natural length. [Assume extension is very less as compared to the length of the wire]

A force of 5 N, making an angle $\theta$ with the horizontal, acting on an object displaces it by 0.4 along the horizontal direction. If the object gains kinetic energy of 1J, the horizontal component of the force is

A tensile force of magnitude $200\text{kN}$ is applied on the prismatic steel rod having radius $10\text{mm}$ and length $1\text{m}$. If Young's modulus of steel is $2\times {10}^{11}{\text{N/m}}^2$, find out the elongation in steel rod.

A unitless quantity

Two balls $A$ and $B$ are flowing through water with same velocity as shown in figure. If radius of ball $A$ is twice the radius of ball $B$, then find the ratio of drag force acting on $A$ and $B$. Assume that Stoke's law is valid.

The magnitude of the displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

The coefficient of self inductance of a solenoid is $0.18$ mH. If a rod of soft iron of relative permeability 900 is inserted in it, then the coefficient of self inductance will become nearly

The acceleration of the system of two bodies over the wedge as shown in the figure is

Two parallel rays are travelling in a medium of refractive index ${\mu }_1=\frac{4}{3}$. One of the rays passes through a parallel glass slab of thickness t and refractive index ${\mu }_2=\frac{3}{2}$. The path difference between the two rays due to the glass slab will be

A ray of light is approaching a set of three mirrors as shown in the diagram. The light ray is approaching the first mirror at an angle of ${45}^{\circ }$ with the mirror surface. How many times will the ray reflect before it exits the system?

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If magnitude of $\overrightarrow{Q}$ is doubled, the new resultant is perpendicular to $\overrightarrow{P}.$ Then $|\overrightarrow{R}|$ equals

A particle of mass $m$ moving with velocity $1\text{m/s}$ collides elastically with another particle of mass $2m$ (initialy at rest). If the incident particle is deflected by ${90}^{\circ }$. The angle $\theta$ made by the heavier mass with the initial direction of motion of mass $m$ will be equal to:

(consider collision to be perfectly elastic)

A body thrown vertically up with a finite speed is caught back after $4\text{sec}$. The speed of the body with which it is thrown up is

(Take $g=10{\text{m/s}}^2$)

A $0.098\text{kg}$ block slides down a frictionless track as shown (Assume no energy loss on the entire track)

The time taken by the block to move from A to B is

Figure shows two projectiles $A$ and $B$ fired simultaneously. Find the minimum distance between them during their flight.

A ball is projected in a direction inclined to the horizontal and it bounces on a horizontal plane. If the range of first rebound is $R$ and coefficient of restitution is $e$, then range of the next rebound is

Carry is running over a circular track of radius $10m$. If he runs $2m$ in $1\text{second}$. Find the angle substended by carry at the center of circular track in $1$ second.

Two blocks of masses $m_A=10\text{kg}$ and $m_B=15\text{kg}$ initially moving in the same direction with velocities of $u_A=3\text{m/s}$ and $u_B=6\text{m/s}$ collide elastically. What is the velocity of the block of mass $10\text{kg}$ after the collision?

The dimensions of universal gravitational constant are

If sum of the roots of a quadratic equation is $8$ and their product is $15$, then the quadratic equation is

A body thrown up along a frictionless inclined plane of angle of inclination ${30}^{\circ }$ covers a distance of 40 m along the plane. If the body id projected with the same speed at an angle of ${30}^{\circ }$ with the ground, it will have a range of

$(Takeg=10m{s}^{-2})$

A body of mass $1kg$ is moving with a velocity $v=10\hat{i}+5\hat{j}$ m/s. What is the angle made by the momentum vector with $x-$ axis?

The level of water in a tank is $5\text{m}$ high. A hole of area $1{\text{cm}}^2$ is made at the bottom of the tank. The rate of leakage of water from the hole is : [Take $g=10{\text{m/s}}^2$]

Evaluate $\frac{25.2\times 1374}{33.3}$. All the digits in this expression are significant.

A gun fires $20$ bullets/sec each of mass $20\text{gm}$, with a muzzle velocity of $50\text{m/s}$. Find the force required to hold the gun in position.

A block placed on a horizontal surface is being pushed by a force F making an angle $\theta$ with the vertical. If the friction coefficient is $\mu$, how much force is needed to get the block just started.