Explore topic-wise InterviewSolutions in Current Affairs.

A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\text{m/s}$. The cartesian equation of its path is $(g=10{\text{m/s}}^2)$

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

One end of a massless spring of spring constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the table is made to rotate at an angular velocity of 2 rad/s, find the elongation of the spring(approximately).

A block of mass $50kg$ moves on a rough horizontal surface with a coefficient of kinetic friction µ = 0.5. If the distance traveled is $20m$, how much work is done by the friction force? (take g = 10 $m/s^{\mathrm{2)}}$

A sinusoidal voltage of peak value $200\text{volt}$ is connected to a diode and resistor $R$ in the circuit shown so that half wave rectification occurs. If the forward resistance of the diode is negligible compared to $R$ then rms voltage (in volt) across $R$ is approximately -

The force exerted by a compression device is given by $F\left(x\right)=kx(x-l)$, where $l$ is the maximum possible compression, $x$ is the compression and $k$ is a constant. The work required to compress the device by a distance $d$ will be maximum when

A projectile is projected from the origin in the $x-y$ plane with a velocity of $60\text{m/s}$ at a${30}^{\circ }$ with the horizontal. Find the position vector of the projectile after $2\text{seconds}$. Take $(g=10{\text{m/s}}^2)$

A U-tube having unequal arm-lengths has water in it. A tuning fork of frequency 440 Hz can set up the air in the shorter arm in its fundamental mode of vibration and the same tuning fork can set up the air in the longer arm in its first overtone vibration. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air =$330m{s}^{-1}$.

What is magnetic intensity and magnetizing (magnetic ) field?

In a children's park a heavy rod is pivoted at the centre and is made to rotate about the pivot so that the rod always remains horizontal. Two kids hold the rod near the ends and thus rotate with the rod (figure 7-E2). Let the mass of each kid be 15 kg, the distance between the points of the rod where the two kids hold it be 3.0 m and suppose that the rod rotates at the rate of 20 revolutions per minute. Find the force of friction exerted by the rod on one of the kids.

A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination, assuming same mass per unit area for the two plates.

The point from where a ball of mass $2\text{kg}$ is projected is taken as the origin of the co-ordinate axes. The $x$ and $y$ components of its displacement are given by $x=6t$ and $y=8t-5t^2$. Find the change in its momentum ( in 𝒌𝒈 𝒎/𝒔) from $t=0$ to $t=2$ seconds.

A small sphere of mass m is dropped from a great height. After it has fallen 100 m, it has attained its terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first 100 m of fall is

Two masses of m1 and m2 (m1>m2) have equal kinetic energies. Which mass will have greater momentum?

what factors does electric field depend on?

How many grams of a liquid of specific heat $0.2{\text{cal/g}}^{\circ }\text{C}$ at a temperature ${40}^{\circ }\text{C}$ must be mixed with $100\text{gm}$ of a liquid of specific heat $0.5{\text{cal/g}}^{\circ }\text{C}$ at a temperature ${20}^{\circ }\text{C}$, so that the final temperature of the mixture becomes ${32}^{\circ }\text{C}$?

The minimum speed ball should have inside a smooth vertical tube when released from a height of $h=2\text{cm}$ as shown in the figure so that it may reach the top of the tube is
(Take $g=10m/s^2$)

A mass M attached to a light spring oscillates with a period of 2 seconds. If the mass is increased by 2 kg the period increases by 1 second. What is the value of M?

A wind with speed $40\text{m/s}$ blows parallel to the roof of a house. The area of the roof is $250{\text{m}}^2$. Assuming that the pressure inside the house is equal to atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho }_{\text{air}}=1.2{\text{kg/m}}^3)$

If $y=e^x\cot \left(x\right)$, then $\frac{dy}{dx}$ will be

The equation of a transverse wave is given by $y=10sin\pi (0.01x-2t)$ where x and y are in cm and t is in second. Its frequency is

A ray parallel to $x$ - axis is incident on a spherical reflecting surface of radius $R$ and the reflected ray becomes parallel to the $y$ - axis as shown. Find the coordinates of point $P$.

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 $15\text{N}$.

A neutral particle (mass m) is at rest in uniform $\overrightarrow{B}$. Due to internal force particle explods into two parts of mass $\frac{m}{4}\&\frac{3m}{4}$. Initial velocity of particle in a plane is perpendicular to $\overrightarrow{B}$. Radius of circular path follwed by particles are $R_1\&R_2$, then $\frac{R_1}{R_2}$

Consider a radioactive sample which is a mixture of two radioactive species; one with a population $N_1$ and mean life of $t_1$ and another with a population $N_2$ and mean life of $t_2$. Then, the effective mean life of the nuclei in the mixture will be

A particle of charge $3.2\times {10}^{-19}C$ travels through a potential difference of ${10}^{-2}$ Volts from rest, the final speed of particle is _______ $(m=1.6\times {10}^{-27}kg)$

A telephonic communication service is working at carrier frequency of $10GHz$. Only $10\%$ of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of $5kHz$ ?

For $\overrightarrow{A}=4\hat{i}+3\hat{j}\&\overrightarrow{B}=\hat{i}+\sqrt{3}\hat{j}$, find angle between $\overrightarrow{A}\times \overrightarrow{B}\&3\overrightarrow{A}+4\overrightarrow{B}$

The relation between $\alpha and\beta$ parameters of a transistor is

An ac source of angular frequency $\omega$ is fed across a resistor r and a capacitor C in series. The current registered is i. If now the frequency of source is changed to $\frac{\omega }{3}$ (but maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$

The waves used for line-of-sight (LOS communication) is

If the optical axis of convex and concave lenses are separated by a distance 5mm shown in the figure. If the coordinates of final image formed by the combination of lenses is (x, y) when the parallel beam of light is incident on convex lens. If origin is at the optical centre of convex lens, $\frac{x}{20y}$ = ___.

Find the acceleration (in $m/s^2$) of the body of mass $20kg$ shown in the figure. Take $g=10m/s^2$.

A child pushes a $2.2\text{kg}$ swing that is initially at rest. The net force on the swing over time is shown below.


What is the swing's speed at $t=40\text{ms}$? Round off the answer to two decimal places.

The coil having one turn is made into coil of two turns. If the same current is passed in both the cases, then the ratio of the magnetic induction at their centers will be

Water pours out at the rate of Q from a tap, into a cylindrical vessel of radius r. find the rate at which the height of water level rises when the height is h.

A block of mass $m$ is connected to another block of mass $M$ by a massless spring constant $k$, the blocks are kept on a smooth horizontal plane and are at rest. The spring is unstretched when a constant force $F$ starts acting on the block of mass $M$ of pull it. Find the maximum extension of the spring.

The potential energy of a particle of mass $5kg$ moving in the x-y plane is given by $U=(-7x+24y)J$ ; $x$ and $y$ being measured in $m$. If the particle starts from origin from rest, the magnitude of the conservative force acting on the particle is

Two spherical balls $A$ and $B$ are connected by the massless rod. The masses of ball $A$ and $B$ are $2\text{kg}$ and $5\text{kg}$. Find the moment of inertia of the system about the axis passing perpendicular to the length of rod as shown in figure bellow.

If an athlete were somehow scaled up proportionally to twice the original size, would he be stronger or weaker?

If | $\overrightarrow{A}$ $\times$ $\overrightarrow{B}$ | = $\sqrt{3}A.B$ , then the value of | $\overrightarrow{A}$ + $\overrightarrow{B}$ | is:

A plane is inclined at an angle $\alpha ={30}^{\circ }$ with respect to the horizontal. A particle is projected with a speed $u=2\text{m/s}$ from the base of the plane, making an angle $\theta ={30}^{\circ }$ with respect to the plane as shown in the figure. The distance from the base (along the inclined plane) at which the particle hits the plane is close to

At certain place on railway track, the radius of curvature of railway track is $200\text{m}$. If the distance between the rails is $1.6\text{m}$, and the outer rail is raised by $0.08\text{m}$ above the inner rail, find the speed of train for which there is no side pressure of the rails.
(Take $g=10{\text{m/s}}^2$)