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For full scale deflection of total $50$ divisions, $50\text{mV}$ voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is $2\text{div/mA}$ will be :

The dimensional formula for intensity of magnetising field and magnetic susceptibility are.

A cyclotron is used to accelerate protons to a kinetic energy of $5\text{MeV}$. If the strength of the applied magnetic field in the cyclotron is $2\text{T}$, the radius of the cyclotron will be

$($Velocity of proton is $3\times {10}^7\text{m/s})$

A uniform cubical block of density ${\rho }_b\left(\text{in g/cc}\right)$ and length a is released from rest from the position where one of its horizontal surface (lower) just touches the water (density ${\rho }_w=1\text{g/cc}$). The time period of oscillation of the block is $({\rho }_b=\frac{2}{3}\text{g/cc},\text{neglect viscosity and surface tension})$

Two planets of equal mass orbit a much more massive star (figure). Planet $m_1$ moves in a circular orbit of radius $1\times {10}^8$ km with period 2 year. Planet $m_2$ moves in an elliptical orbit with closest distance $r_1=1\times {10}^8$ km and farthest distance $r_{2}1.8\times {10}^8$km, as shown. Using the fact that mean radius of an elliptical orbit is the length of the semi-major axis, find the period of $m_2^{{}^{\prime }}$ s orbit.

A toy cart is tied to the end of an unstretched string of length $‘l^{\prime }$, when revolved, the toy cart moves in horizontal circle with radius $‘2l^{\prime }$ and time period $T_1$. If it is speeded until it moves in horizontal circle of radius $‘3l^{\prime }$ with period $T_2$, relation between $T_1$ and $T_2$ is (Hooke’s law is obeyed)

A cycle wheel of radius 0.4 m completes one revolution in one second then the acceleration of a point on the cycle wheel will be

Choose the correct dimensional formula of $5CV$.

($C$ is capacitance and $V$ is potential difference)

An electron $(e,m)$ is revolving in a circular orbit about the nucleus of an atom. Find a relationship between the orbital magnetic dipole moment $\overrightarrow{\mu }$ and the angular momentum $\overrightarrow{L}$ of the electron about the centre of its orbit.

A propped cantilever beam of span 'L' is loaded with uniformly distributed load of intensity w/unit length, all through the span. Bending moment at the fixed end is

An electron $(-e,m)$ is given velocity $V_o$ along a uniform electric field $\overrightarrow{E}$. After how much time, electron will return to its original position?

The coil of a galvanometer has $500$ turns, and each turn has an average area $3\times {10}^{-4}{\text{m}}^2$. If current of $0.5\text{A}$ pass through it and torque of $1.5\text{Nm}$ is generated in the coil. Find the strength of the magnetic field and torsional constant of coil if the angle of deflection is $\frac{\pi }{2}$.

A current is flowing through a thin cylindrical shell of radius $R$. If energy density in the medium, due to magnetic field, at a distance $r$ from the axis of the shell is equal to $U$, then which of the following graphs is correct?

A black metal foil is warmed by radiation from a small sphere at temperature $‘T^{\prime }$ and at a distance $‘d^{\prime }$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled, the power received by the foil will be :

Find the energy liberated in the reaction: ${}^{223}Ra{\to }^{209}Pb{+}^{14}C$

The atomic masses needed are as follows:

$\underset{223.018u}{{}^{223}Ra}$ $\underset{208.981u}{{}^{209}Pb}$ $\underset{14.003u}{{}^{14}C}$

In a new system of units, the fundamental quantities mass, length and time are replaced by acceleration $a$, density $\rho$ and frequency $f$. The dimensional formula for force in this system is

The value of $\underset{0}{\overset{\pi /2}{\int }}{\sin }^{10}x\cdot {\cos }^{2}xdx$ is

In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value $a_0$ at the end of $100$ oscillations. When the oscillator completes $200$ oscillations, its amplitude must be

(a) A circular coil of 30 turns and radius 8.0 cm carrying a
current of 6.0 A is suspended vertically in a uniform horizontal
magnetic field of magnitude 1.0 T. The field lines make an angle of
60º
with the normal of the coil. Calculate the magnitude of
the counter torque that must be applied to prevent the coil from
turning.

(b) Would your answer change, if the circular coil in (a)
were replaced by a planar coil of some irregular shape that encloses
the same area? (All other particulars are also unaltered.)

An electric heater emits 1000 W of thermal radiation. The coil has a surface area of 0.020 $m^2$. Assuming that the coil radiates like a blackbody, find its temperature. $\sigma =6.00\times {10}^{-8}W/m^2-K^4$.

A body of mass $2\text{kg}$ is moving with constant velocity $10\text{m/s}$ on a straight line $3x+4y+5=0$. Calculate its angular momentum with respect to origin.

A girl walks $4\text{km}$ towards west, then she walks $3\text{km}$ in a direction ${30}^{\circ }$ east of north and stops. Girl's displacement from her initial point of departure is