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A metallic shell has a point charge $q$ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force ?

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

Two thin identical rods are arranged along X-axis and Y-axis with their ends meeting at the origin. If $I_x,I_{y}and{I}_z$ are the moments of inertia of the system about the X, Y and Z axes respectively, then which of the following are correct?

Two prisms of identical geometrical shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by ${1.0}^{\circ }$ when passes symmetrically through this combination. What is the angle of the prisms ?

The
normal activity of living carbon-containing matter is found to be
about 15 decays per minute for every gram of carbon. This activity
arises from the small proportion of radioactive

present with the stable carbon isotope
. When the organism is dead, its interaction with the atmosphere
(which maintains the above equilibrium activity) ceases and its
activity begins to drop. From the known half-life (5730 years) of,
and the measured activity, the age of the specimen can be
approximately estimated. This is the principle of
dating
used in archaeology. Suppose a specimen from Mohenjodaro gives an
activity of 9 decays per minute per gram of carbon. Estimate the
approximate age of the Indus-Valley civilisation.

A body moves in a circle of radius $1\text{m}$, whose speed varies with time $t$(in $s$) as $v=2t^{2}m{s}^{-1}$. Find the net acceleration at $t=2\text{seconds}$.

Two mating spur gears have $40$ and $120$ teeth respectively. The pinion rotates at $1200rpm$ and transmits a torque of $20N.m.$. The torque transmitted by gear is

A capacitor stores $50\mu \text{C}$ charge when connected across battery. When the gap between the plates is filled with a dielectric, a charge of $100\mu \text{C}$ flows through the battery. Find the dielectric constant of the material inserted.

Why does an electron have negative potential energy ??

Two blocks $A$ and $B$ having the same mass collide elastically with each other. the velocity of block $A$ before the collision is $10\text{m/s}$. If block $A$ comes to rest after collision, then what was the velocity of block $B$ before the collision?

Two non - zero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. Find angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

A satellite of mass $m$ revolves round the earth of mass $M$ in a circular orbit of radius $r$ with an angular velocity $\omega$. If the angular velocity is $\omega /8$ then the radius of the orbit will be

A car is moving along a straight horizontal road with a speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$, the shortest distance in which the car can be stopped is

A gas expand adiabatically at constant pressure such that

$T\propto V^{-3/4}$. The value of $\gamma \left(\frac{C_p}{C_v}\right)$ of the gas will be:

Experimental investigations show that the intensity of solar radiation is maximum for a wavelength $480nm$ in the visible region. Estimate the surface temperature of the sun. Given Wien's constant, $b=2.88\times {10}^{-3}mK$.

Find the tension in the string connecting block of mass $M$ and ring of mass $m$ at the instant shown. Assume all surfaces to be frictionless and the ring is constrained to move along the wire only. $M=25\text{kg};m=9\text{kg}$ and $g=10{\text{m/s}}^2$

Which of the following graph of electrostatic force between two positive charges $\left(F_e\right)$ vs $r^2$, is a correct representation?

($r$ is the distance between two charges)

Velocity of sound in air is $320\text{m/s}$. A pipe closed at one end has a length of $1\text{m}$, neglecting end corrections. Find the frequency(s) for which the air column in the pipe can resonate.

Difference between triangle law and triangle law of vector addition

If instead of dropping, I threw a ball down at some velocity u,near the surface of the earth, the ratio of the distances covered in the 1st , 2nd and 3rd second (not after n seconds) will be ?

At some temperature T, a bronze pin is a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when

A magnetic needle of pole strength $20\sqrt{3}\text{Am}$ is pivoted at its center. Its $N$-pole is pulled eastward by a string. The horizontal force required to produced a deflection of ${30}^{\circ }$ from magnetic meridian $[\text{Take}{B}_H={10}^{-4}\text{T}]$ is

1. 24.87

A pump on the ground floor of a building can pump up water to fill a tank of volume 30 $m^3$ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?

A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?

A capacitor of capacitance 1 μF is charged to a potential of 1 V. It is connected in parallel to an inductor of inductance 10^-3 H. The maximum current that will flow in the circuit has the value