Explore topic-wise InterviewSolutions in Current Affairs.

A fisherman hooks an old log of wood of weight 12N and volume 1000 $c{m}^3$. He pulls the log half way out of water. The tension in the string at this instant is

What is the direction of instantaneous acceleration?

In uniform circular motion

The total number of magnetic lines of force crossing a surface normally is termed as

A thick uniform rubber rope of density $1.5gc{m}^{-3}$ and Young's modulus $5\times {10}^{6}N{m}^{-2}$ has a length of 8 m. When hung from the ceiling of a room, the increase in length of the rope due to its own weight will be equal to

When a force is applied at one end of an elastic wire, it produces a strain $ϵ$ in the wire. If $Y$ is Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

The coefficient of $x^m$ in $(1+x{)}^k+(1+x{)}^{k+1}+..............+(1+x{)}^n,$$(k\le m\le n)$, is given by:

A ray of light is incident at an angle $i$ on a surface of a thin prism of angle $A$, which emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, the angle of incidence $i$ is nearly equal to :

A dimensionless quantity ______.

A particle executes a SHM of time period T. The time taken by the particle to go directly from its mean position to half the amplitude.

Two forces 3N and 2 N are at an angle q such that the resultant is R. The first force is now increased to 6N and the resultant become 2R. The value of q is

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance, its velocity $v$ varies with height $h$ above the ground as.

Four point masses $2\text{kg},3\text{kg},5\text{kg}$ and $7\text{kg}$ respectively are placed at the four corners $A,B,C$ and $D$ of a square of side $4\text{m}$. The position of $COM$ will be

A heavy steel ball of mass greater than 1 kg moving with a speed of 2 $mse{c}^{-1}$ collides head-on with a stationary ping-pong ball of mass less than 0.1 g. The collision between them was elastic. After the collision the ping-pong ball moves approximately with a speed of

Two bombs have been fired simultaneously from cannon $A$ and $B$, which are similar and have a fixed barrel inclination of ${45}^{\circ }$. The cannons are facing each other and have a horizontal separation of $400\text{m}$, bombs are fired towards each other at a speed of $20\sqrt{2}\text{m/s}$. Find the time when both shells collide in air.

Radioactive isotopes are produced in a nuclear physics experiment at a constant rate $\frac{dN}{dt}$ = R. An inductor of inductance 100 mH, a resistor of resistance 100 $\Omega$ and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that $\frac{i}{N}$ remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t Find the half-life of the isotope.

If work function of metal is 3eV then threshold wavelength will be

Angle of prism is ${30}^{\circ }$ and its refractive index is $\sqrt{2}$ and one of the refracting faces is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

A rubber rope of length $7\text{m}$ is hung from the ceiling of a room. What is the increase in length of the rope due to its own weight? (Given: Young's modulus of elasticity of rubber = $5\times {10}^6{\text{N m}}^{-2}$ and density of rubber = $1.5\times {10}^3\frac{\text{kg}}{{\text{m}}^3}$ and $g=10\frac{\text{m}}{{\text{s}}^2}$)

A thin rod of length $L$ is lying along the $x-$ axis with its ends at $x=0$ and $x=L$. Its linear density (mass/length) varies with $x$ as $\lambda =k{\left(\frac{x}{L}\right)}^n$, when $n$ can be zero or any positive number. If the position $x_{\text{cm}}$ of the centre of mass of the rod is plotted against ${}^{\prime }{n}^{\prime }$, which of the following graphs best approximates the dependence of $x_{\text{cm}}$ on $n$?

For a given A.C voltage $V=V_0\sin \omega t$, if $V_1$ is average voltage of half cycle and $V_2$ is rms voltage, then $\frac{V_1}{V_2}$ is

Find the dimensions of

(a) angular speed $\omega$

(b) angular acceleration $\alpha$

(c) torque $\Gamma$ and

(d) moment of interia I.

Some of the equations involving these quantities are

$\omega =\frac{{\theta }_2-{\theta }_1}{t_2-t_1}$,

$\alpha =\frac{{\omega }_2-{\omega }_1}{t_2-t_1}$

$\Gamma =Fj$ and $I=m{r}^2$.

The symbols have standard meanings.

A body is projected with an initial velocity of 50 $m{s}^{-1}$ at angle 53 with the horizontal. Calculate the velocity when it reaches a height of 40 m.

A pendulum bob of mass $10g$ is attached to a rod of length $2m$ and is allowed to move in the vertical circle. Find the minimum velocity of bob at the bottom of the circle so that the bob completes the circle.

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

A cylindrical tank has a hole of $1c{m}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70c{m}^3/sec$. then the maximum height up to which water can rise in the tank is

A device is designed in such a way that it displays green light whenever its speed is increasing and a blue light when the speed is decreasing. If the device is performing SHM with a time period of 12s and it starts from the extreme position, when is the device green?

A man can see only between 75 cm and 200 cm. The power of lens to correct

the near point will be

The drift velocity in Cu wire if it has 1A current through $2m{m}^2$ cross – section is (free electron density is $8.5\times {10}^{22}c{m}^{-3}$ ).

A block performs SHM and its equation is given as $x=4+5sin\pi t$. Which of these would be its correct representation?

The figure shows a cross -section of along thin ribbon of width b that is carrying a uniformly disturbed total current i into the page. Calculate the magnitude and direction of the magnetic field $\overrightarrow{B}$ at a point P in the plane of the ribbon at a distance afrom its edge.

There is a square wire frame ABCD of side equal to b and whose centre is at a distance OP = $\frac{b}{2}$ from an infinite line charge (parallel to BC and AD) with linear charge density $\lambda$ then [plane of the frame is perpendicular to line OP.]

Penguins huddling: To withstand the harsh weather of the Antarctic, emperor penguins huddle in groups. Assume that a penguin is a circular cylinder with a top surface area a =0.26 $m^2$ and height h = 90 cm. Let $P_r$ be the rate at which an individual penguin radiates energy to the environment (through the top and the sides); thus $N{P}_r$ is the rate at which N identical, well-separated penguins radiate. If the penguins huddle closely to form a huddled cylinder with top surface area Na and height h, the cylinder radiates at the rate $P_h$. If N = 1000, by what percentage does huddling reduce the total radiation loss?

The displacement of the particle is given by $x=3t^3-2t^2+5$ in $\text{m}$. The acceleration of the particle at $4\text{sec}$ is

A block of mass $m$ is pushed towards a movable wedge of mass $nm$ and height $h$, with a velocity $u$. All surfaces are smooth. The minimum value of $u$ for which the block reaches the top of the wedge is -

If the gauge pressure at the bottom of a water tank is $2.7\text{kPa}$, then what is the depth of the water in the tank?
[Take $g=10{\text{m/s}}^2$]

In the circuit shown in figure, the rms current $I_1,I_2\&I_3$ , are altered by varying frequency $f$ of the oscillator. The output voltage of the oscillator remains sinusoidal and has a fixed amplitude. Which curves in figure correctly indicate the variation with frequency of currents $I_1,I_2\&I_3$?

A particle is performing S.H.M with time period $T$. Find the shortest time taken by the particle to go from the mean position to an extreme position.

Two condensers, one of capacity $C$ and other of capacity $\frac{C}{2}$ are connected to a $V$ - volt battery as shown in the figure. The work done in charging both the condensers fully is

The change in Gravitational potential energy when a body of mass $m$ is raised to a height $nR$ from the Earth’s surface is ($R$= radius of the earth, $g$= acceleration due to gravity on the surface of Earth)

The ratio of the speed of sound in nitrogen gas to that in helium gas at 300 K is

Find the frictional force between the two blocks. Take $g=10{\text{m/s}}^2$.

A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r={\lambda }_1/{\lambda }_2$, is given by

In the given series LCR circuit, the voltmeter and ammeter readings are

The main difference in the phenomenon of interference and diffraction is that:

A composite slab have two layers of different materials, having thermal conductivity $k_1$ and $k_2$. If each layer has same thickness, then what is the equivalent thermal conductivity of the slab?

In the figure shown, find the angle $\theta$ for which the pulling force is $\mu mg$ where $\mu$ is the coefficient of friction between the two surfaces

A beaker containing a liquid of density $\rho$ moves up with an acceleration ${}^{\prime }{a}^{\prime }$. The pressure in the liquid at a depth $h$ below the free surface of the liquid is (consider atmospheric pressure to be $P_0$)

Why is magnetic field always perpendicular to velocity?

Is there any case where magnetic field is not perpendicular to velocity? How?