Explore topic-wise InterviewSolutions in .

An electric field is expressed as $\overrightarrow{E}=2\hat{i}+3\hat{j}$. Find the potential difference $(V_A-V_B)$ between two points A and B whose position vectors are given by $r_A=\hat{i}+2\hat{j}$ and $r_B=2\hat{i}+\hat{j}+3\hat{k}.$

Two wires having different mass densities are soldered together end to end, then stretched under tension $T$. The wave speed in the first wire is twice that in the second wire and the amplitude of incident wave is $a$. Assuming no energy losses in the wire, find the fraction of the incident power that is reflected.

The equation of the line making ${37}^{\circ }$ with $x-axis$ and passing through $(2,-4)$ is

[Hint:- $\tan {37}^{\circ }=\frac{3}{4}$]

Find $\overrightarrow{A}\times \overrightarrow{B}$, if $\overrightarrow{A}=\hat{i}+4\hat{k}\text{and}\overrightarrow{B}=-\hat{j}$?

5 identical condensers are connected as shown in the fig. If the effective capacity between A and B is $6\mu F$, the capacity of each condenser is

A ball of mass ${}^{\prime }{m}^{\prime }$ moving horizontally which velocity ${}^{\prime }{u}^{\prime }$ hits a wedge of mass ${}^{\prime }{M}^{\prime }$. the wedge is situated on a smooth horizontal surface. If after striking wedge the ball starts moving in vertical direction and the wedge starts moving in horizontal plane. Calculate the coefficient of restitution $e$.

Coefficient of linear expansion of brass and steel rods are ${\alpha }_1$and ${\alpha }_2$ . Length of brass and steel rods are $l_1$ and $l_2$ respectively. If $l_2–l_1$ is maintained same at all temperatures, then find the ratio of ${\alpha }_1$ to ${\alpha }_2$.

A particle of mass $m=4\text{kg}$ is projected with a speed of $u=10\text{m/s}$ at an angle of ${45}^{\circ }$ with the horizontal. The particle explodes in mid air when it is at the maximum height. One component weighing $1\text{kg}$ comes to rest after the explosion and the other component of mass $3\text{kg}$ moves away. Find the distance where the $3\text{kg}$ mass component strikes the ground from the initial position (projection point). [Take $g=10{\text{m/s}}^2$]

The balloon, the light rope and the monkey shown in figure are at rest in the air. If the monkey reaches the top of the rope , by what distance does the ballon descent? Mass of the balloon = M , mass of the monkey = m and the lenght of the rope ascended by the monkey = L.

The strain energy stored in a body of volume $V$ due to shear strain $\varphi$ is (shear modulus is $G$)

Find the x coordinate of the centre of mass of the arrangement of three uniform rods kept in horizontal plane, as shown in figure. (Consider mass and length of each rod is m and l respectively)



चित्र में दर्शाए अनुसार क्षैतिज तल में रखी एक जैसी तीन छड़ों के समंजन के द्रव्यमान केन्द्र का x निर्देशांक ज्ञात कीजिए। (माना प्रत्येक छड़ का द्रव्यमान तथा लम्बाई क्रमशः m तथा l हैं)

A motorcyclist drives from place $A$ to $B$ with a uniform speed of $30\text{km/h}$ and returns from place $B$ to $A$ with a uniform speed of $20\text{km/h}$. Find his average speed.

Two neutral spheres are kept side by side, now 150 electrons are transferred from one to other, find the magnitude of charge on one sphere.

A Driver is driving a car at speed of 72 km/hr on road. He sees a boy on road at a distance of 48 m from him. If his reaction time is 0.4 sec, find minimum retardation required to save the boy.

The system shown in the figure is released from rest with the mass $2\text{kg}$ in contact with the ground. The pulley and spring are massless, and friction is absent everywhere. Then, find the speed of the $5\text{kg}$ block when the $2\text{kg}$ block leaves contact with the ground (force constant of the spring $k=40{\text{Nm}}^{-1}$ and $g=10{\text{ms}}^{-2}$)

The vector sum of two forces P and Q is minimum when the angle between them is

The acceleration of the particle moving in positive $x-$direction with an initial velocity of $10m/s$ is $3m/s^2$. Its velocity at $t=4sec$ is

A thin wire of length $99\text{cm}$ is fixed at both ends. The wire has some tension and is divided into three segments of lengths $l_1,l_2$, and $l_3$ as shown in the figure. If these segments are made to vibrate, with their fundamental frequencies respectively in the ratio $1:2:3$, then the lengths $l_1,l_2,l_3$ respectively are (in $\text{cm}$):

The proportional limit of steel is $8\times {10}^8{\text{N/m}}^2$ and its young modulus is $2\times {10}^{11}{\text{N/m}}^2.$ The maximum elongation, a one meter long steel wire can be given without exceeding the proportional limit is

A horizontal rope of $1\text{m}$ length, having a mass $100\text{g}$, is fixed at one end and is tied to a light string at the other end. Find the frequency and wavelength of the fifth overtone, if the tension in the string is $40\text{N}$.

A particle is projected with a speed $u$ at an angle $\theta$ with horizontal from point $A$. It strikes elastically with a vertical wall at height $h/2$. It rebounds and reaches maximum height $h$ and falls back on the ground at point $B$ as shown in Figure. Distances from $A$ to wall and from wall to $B$ are $x_1$ and $x_2$, and time to cover is $t_1$ and $t_2$ respectively. Match the values in column I with the expressions in column II.





$$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.}\sqrt{2}& \text{a.}\frac{x_2-x_1}{x_2+x_1}\text{or}\frac{x_2+x_1}{x_2-x_1}\\ \text{ii.}\frac{1}{\sqrt{2}}& \text{b.}\frac{t_2-t_1}{t_2+t_1}\text{or}\frac{t_2+t_1}{t_2-t_1}\\ \text{iii.}1& \text{c.}\frac{u\sin \theta }{g(t_2+t_1)}\\ \text{iv.}\frac{1}{2}& \text{d.}\frac{u\cos \theta (t_1+t_2)}{x_1+x_2}\end{array}$$

A force F is applied horizontally to a block A of mass $m_1$ which is in contact with a block B of mass $m_2$, as shown in the figure. If the surfaces are frictionless, the force exerted by A on B is equal to

A uniform rod of mass $2\text{kg}$ is hanging from a thread attached at the midpoint $\left(\text{O}\right)$ of the rod. A block of mass $m=6\text{kg}$ hangs at the left end of the rod and a block of mass $M$ hangs at the right end at a distance of $30\text{cm}$ from the mid point $\left(\text{O}\right)$. If the system is in equilibrium, calculate the mass $\left(M\right)$, given that overall length of the rod is $100\text{cm}$. Take $g=10{\text{m/s}}^2$.

A film of water is formed between two straight parallel wires each $10\text{cm}$ long and at separation $0.5\text{cm}$. Calculate the work required to increase $1\text{mm}$ distance between the wires. Surface tension of water$=72\times {10}^{-3}\text{N/m}$.

Two equal spheres $A$ and $B$ lie on a smooth horizontal circular groove at opposite ends of a diameter. At time $t=0$, $B$ is projected along the groove and it first impinges on $A$ at time $t=T_1$ and again at time $t=T_2$. If $e$ is the coefficient of restitution, the ratio $\frac{T_2}{T_1}$ is

Two discs are rotating about their axes, normal to the plane of the discs and passing through the centre of the discs. Disc $D$ has $2\text{kg}$ mass and $0.2\text{m}$ radius and initial angular velocity of $50\text{rad/s}$. Disc $D_2$ has $4\text{kg}$ mass, $0.1\text{m}$ radius and initial angular velocity of $200\text{rad/s}$. The two discs are brought in contact face to face with their axes of rotation coincident. The final angular velocity (in $\text{rad/s}$) of the system is

In the below figure, a square loop consisting of an inductor of inductance L and resistor of resistance R is placed between two long parallel wires. The two long straight wires have time-varying current of magnitude $I=I_{0}cos\omega t$ A but the directions of current in them are opposite.



Total magnetic flux in this loop is

A crate is on the flat surface of a truck of coefficient of static friction ${\mu }_s=0.8$ and coefficient of kinetic friction ${\mu }_k=0.7$. The coefficient of kinetic friction between the truck tires and the road surface is $0.9$. If the truck suddenly stops from an initial speed of $15m/s$ with maximum braking (wheels skidding), determine the displacement of the crate before it comes to rest.

The surface tension of soap solution is $0.03\text{N/m}$. The work done in blowing to form a soap bubble of surface area $40{\text{cm}}^2$ is:

A ball rolls off the top of a stairway horizontally with a velocity of $4.5{\text{ms}}^{-1}$. Each step is $0.2\text{m}$ high and $0.3\text{m}$ wide. If $g$ is $10{\text{ms}}^{-2}$, then the ball will strike the edge of $n^{th}$ step, where $n$ is equal to

Each branch in the following circuit has a resistance $R$. The equivalent resistance of the circuit between two points $A$ and $B$

Velocity vs displacement graph for a body is shown in the figure.



Find the acceleration of body when it's displacement is $10\text{m}$, considering $1\text{D}$ motion along a straight line.

In the figure, all surfaces are smooth. Find the acceleration of the body and the force exerted by the floor on the body. (Take $g=10m/s^2$)

An electron is projected as shown in the figure, with kinetic energy K, at an angle $\theta ={45}^{\circ }$

between two charged plates. Ignore the gravity.

At what distance from the starting point will the electron strike the lower plate?

The pulley and block arrangement is as shown in the figure.



If string is massless and inextensible, pulley and surfaces are frictionless. Find the horizontal component of the acceleration of COM for the system of blocks. Take $g=10{\text{m/s}}^2$.

An object$\left(O\right)$ is placed at a distance $20\text{cm}$ from a convex mirror. If a plane mirror is also kept at a distance of $12\text{cm}$ from the same object as shown, image$\left(I\right)$ formed by plane mirror is at the same point at which image is produced by the convex mirror. The focal length of the convex mirror is

An aircraft flies at $400km/h$ in still air. A wind of $200\sqrt{2}km/h$ is blowing from the south. The pilot wishes to travel from $A$ to a point $B$ north-east of $A$. The direction he must steer is

The graph shown below represents the variation of the force as a function of position for a body.





Find out the work done by the force in moving the body from $x=3\text{m}$ to $x=7\text{m}$.

A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=asin(\omega t+\frac{\pi }{6}).$ After the elapse of what fraction of the time peirod, the velocity of the point will be equal to half of its maximum velocity?

A particle is travelling on the x-axis. Its velocity time graph is given:

Which of the following graphs represent the same motion?

A galvanometer shows a reading of $0.65\text{mA}$. When a galvanometer is shunted with a $4\Omega$ resistance, the deflection is reduced to $0.13\text{mA}$. If the galvanometer is further shunted with a $2\Omega$ wire, the new reading will be (the main current remains the same)

An exhaust fan is rotating with an angular velocity of $216\text{rad/min}$. When it is switched off, it is observed that the angular retardation of the fan is $\alpha =\frac{3}{2}\sqrt{t}{\text{rad/min}}^2$. The time taken by the fan to stop completely is

The density of air at $NTP$ is $1.3\text{g/L}$. Assuming air to be diatomic with $\gamma =1.4$, calculate the velocity of sound in air at ${27}^{\circ }\text{C}$.

Which of the following is not possible?

There is a flat uniform triangular plate ABC such that $AB=4\text{cm},BC=3\text{cm}$ and $\angle ABC={90}^{\circ }$ as shown in the figure. The moment of inertia of the plate about AB, BC and CA is $I_1,I_2$ and $I_3$ respectively. The incorrect statement is