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Light with an average flux of $20{\text{W/cm}}^2$ falls on a non-reflecting surface at normal incidence having area $20{\text{cm}}^2$. The energy recieved by the surface during timespan of $1\text{minute}$ is :

A student uses a simple pendulum of exactly 1 m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 s for this and records 40 s for 20 oscillations. For this observation, which of the following statements is true?

The second order Bragg diffrction of $X-rays$ with $\lambda =1.00A^{\circ }$ from a set of parallel planes in a metal occurs at an angle ${60}^{\circ }.$ The distance between the scattering planes in the crystal is

An inclined plane makes an angle ${30}^{\circ }$ with the horizontal. A groove $OA=5\text{m}$ cut in the plane makes an angle ${30}^{\circ }$ with $OX$. A short smooth cylinder is free to slide down the influence of gravity. Find the time taken by the cylinder to reach from $A$ to $O$.

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

Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are $M{L}^2{I}^{-2}{T}^{-3}$ and $M{L}^2{T}^{-3}{I}^{-1}$ respectively.

If an object at absolute temperature $\left(T\right)$ radiates energy at rate $R$, then select correct graph.

A ring of external and internal radii $r_1$ and $r_2$ just touches the horizontal surface of a liquid of surface tension $\sigma$. The force required to pull the ring away from the surface is

Which one of the following is the correct $PVvsP$ plot at constant temperature for an ideal gas? ($P$ and $V$ stands for pressure and volume of the gas respectively)

A $50\text{N}$ force is applied to the body of $2\text{kg}$. This applied force maintains the velocity of the body at $2\text{m/s}$. If the body moves in perpendicular direction to the applied force, find the power delivered by the force.

An object is at a temperature of ${400}^0$ C. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible

Two blocks are connected by a string, as shown in the figure. They are released from rest. Find the speed after they have moved a distance x.$\mu$ is the coefficient of kinetic friction between the upper block and the surface. Assume that the pulley is massless and frictionless.

Distinguish between the average speed and the average velocity.

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane in circular path with $O$ as centre. If the velocity of the outermost particle $v_0$, then the ratio of tensions in the three sections of the string is

Take the breakdown voltage of the Zener diode used in the given circuit as $6\text{V}$ for the input voltage shown in figure below, the time variation output voltage is-

(graphs drawn schematic and not to scale)

A copper wire of cross-sectional area $0.01{\text{cm}}^2$ is under a tension of $20\text{N}$. Find the decrease in the cross-sectional area. Young's modulus and Poisson's ratio of copper are $1.1\times {10}^{11}{\text{N/m}}^2$ and $0.32$ respectively.

Four point charges $-q,+q,+q$ and $-q$ are placed on $y-$ axis at $y=-2d,y=-d,y=+d$ and $y=+2d,$ respectively. The magnitude of the electric field $E$ at a point on the $x-$ axis at $x=D,$ with $D>>d,$ will behave as-

A circular platform is free to rotate in a horizontal plane about vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ${\omega }_0$. When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform). The angular velocity of the platform $\omega \left(t\right)$ will vary with time t as

The velocity distribution for the flow over a flat plate is given by $u=2y-y^2$ in which $u$ is the velocity in $\text{m/s}$ at a distance $y\text{metres}$ above the plate. Determine the shear stress at $y=0.15\text{m}$. Take dynamic viscosity of the fluid as $8.5\text{poise}$.

A ship floats with ${\frac{1}{3}}^{rd}$ of its volume outside. when its in water. When it floats in another liquid, ${\frac{2}{3}}^{rd}$ of its volume is outside the liquid. What is the relative density of the liquid?

A round bar ACB of length 2L as shown in figure rotates about an axis through the midpoint C with constant angular speed $\omega$ (rad/s) . The material of the bar has weight density $\gamma$. The expression for the tensile stress ${\sigma }_x$ in the bar as a function of the distance x from the midpoint C is

A body is projected at $t=0$ with a velocity $10{\text{ms}}^{-1}$ at an angle of ${60}^{\circ }$ with the horizontal. The radius of curvature of its trajectory at $t=1\text{s}$ is $R$. Neglecting air resistance and taking acceleration due to gravity $g=10{\text{ms}}^{-2}$, the value of $R$ is:

$(\text{Take:}\tan {15}^{\circ }=0.268;\cos {15}^{\circ }=0.966)$

In a Young's double slit experiment, the width of one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

A parallel plate capacitor having capacitance $12\text{pF}$ is charged by a battery to a potential difference of $10\text{V}$ between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant $6.5$ is placed between the plates. The work done by the capacitor on the slab is:

Let $x_1,x_2,x_3,x_4$ be four non-zero numbers satisfying the equation ${\tan }^{-1}\frac{a}{x}+{\tan }^{-1}\frac{b}{x}+{\tan }^{-1}\frac{c}{x}+{\tan }^{-1}\frac{d}{x}=\frac{\pi }{2}$. Which of the following relations hold(s) good ?

Two waves $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\varphi )$ are superimposed such that the resultant amplitude of oscillation is $\sqrt{2}A$, then the value of $\varphi$ is

A proton is rotating along a circular path of radius $0.1\text{m}$ under a centrifugal force of $4\times {10}^{-13}\text{N}$. If the mass of proton is $1.6\times {10}^{-27}\text{kg}$, the angular velocity of rotation is (in rad/s)

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is

In neon gas discharge tube 2.9*10^18 Ne+ ions move to the right through a cross section of the tube each second while 1.2*10^18 electrons move to the left this time. the electronic charge is 1.6*10^-19 coulomb. what is the net electric current in the tube?