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A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is

If the incident ray is stationary, but the plane mirror rotates by an angle of ${30}^{\circ }$, then the reflected ray gets rotated by .

A charged particle of mass $1.0\text{g}$ is suspended through a silk thread of length $40\text{cm}$ in a horizontal electric field of $4\times {10}^4\text{N/C}$. If the particle stays at a distance of $24\text{cm}$ from the vertical wall in equilibrium, find the charge on the particle.

An object is placed in front of a convex mirror at a distance of $50\text{cm}$. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30\text{cm}$, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

A body moves with a uniform acceleration. The velocity at one point A is 10 m/s and at a later point B is 20 m/s. If the time taken to move from A to B is 20 seconds, calculate the distance AB.

A turn table is rotating about the fixed vertical axis. A particle of mass $m$ is lying on a table at rest with respect to the table. An observer is standing over a block of mass $M$ moving with an acceleration $a$. Find the magnitude of pseudo-force on a particle of mass $m$ as observed by the observer. (Given a body is subjected to an acceleration called centripetal acceleration directed towards the centre when it is rotating and is equal to $r{\omega }^2$ )

In the Bohr model of hydrogen atom, the electron is treated as a particle going in a circle with the centre at the proton. The proton itself is assumed to be fixed in an inertial frame. The centripetal force is provided by the Coloumb attraction. In the ground state, the electron goes round the proton in a circle of radius $5.3\times {10}^{-11}m.$ Find the speed of the electron in the ground state. Mass of the electron = $9.1\times {10}^{-31}$ kg and charge of the electron = 1.6 \times 10^{-19}C.

The given diagram is a cross-sectional view of coaxial cable. The central conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is further surrounded by another rubber layer. Current in the inner conductor is $1\text{A}$ directed out of the page, and current in the outer conductor is $3\text{A}$ into the page. The ratio of magnitude of magnetic field at point $\text{a}$ to that at point $\text{b}$ will be -

The relationship between the force f(t) and the displacement x(t) of a spring-mass system with a mass M, viscous damping D and spring constant K,



$M\frac{d^{2}x\left(t\right)}{d{t}^2}+D\frac{dx\left(t\right)}{dt}+Kx\left(t\right)=f\left(t\right)$



X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M= 0.1, D = 2, K= 10 in appropriate units, the transfer function

$G\left(s\right)=\frac{X\left(s\right)}{F\left(s\right)}\text{is}$

Two plane mirrors, $\text{A}$ and $\text{B}$ are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ at a point just inside one end of $\text{A}.$ The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is-

A date with a rate of 400 kbps is to be transmitted using M-ary PSK modulation through a channel whose bandwidth is $100kHz.$ If the baseband modelling of the data is done by a raised cosine filter with a roll-off factr of 0.50, then the minimum value of 'M' required for feasible transmission will be

About
5% of the power of a 100 W light bulb is converted to visible
radiation. What is the average intensity of visible radiation

(a)
at a distance of 1 m from the bulb?

(b)
at a distance of 10 m?

Assume
that the radiation is emitted isotropically and neglect reflection.

Charge $Q$ is distributed on two metallic spheres having radii $R$ and $3R$ such that both spheres have equal charge density then charge on smaller sphere is

A particle is projected upwards with a velocity of $100\text{m/sec}$ at an angle of ${60}^{\circ }$ with the vertical. Find the time when the particle will move perpendicular to its initial direction taking $g=10{\text{m/sec}}^2$.

If the electric flux entering and leaving an enclosed surface respectively is ${\varphi }_1$ and ${\varphi }_2$ the electric charge inside the surface will be

Round the clock cooling of an apartment having a load of $300MJ/day$ requires an air conditioning plant of capacity about

An $\text{LCR}$ series circuit containing a resistance of $120\Omega$ has angular resonance frequency $4\times {10}^5\text{rad/s}$. At resonance, the voltage across resistance and inductance are $60\text{V}$ and $40\text{V}$ respectively. Then the values of $\text{L}$ and $\text{C}$ are respectively.

Between two isotherms at temperatures $2T$ and $T$, a process $ABCD$ is performed with an ideal monatomic gas. $AB$ and $CD$ are adiabatic expansion processes and $BC$ is isobaric expansion process. The average molar specific heat capacity of the overall process with be

A vibratory body of mass 150 kg supported on springs of total stiffness 1050 kN/m has rotating unbalance force of 525 N at speed of 6000 rpm. If the damping factor is 0.3.



Phase angle of vibration is

A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of $-$ve $x-$axis. The parameters of the waves are $A,\omega$ and $k$. The particle at $x=\frac{\lambda }{4}$ executes the motion $y\left(t\right)=A\sin \omega t$. Possible equation of the wave is

An object is placed at a distance of $20\text{cm}$ from a concave mirror and its real image is formed at distance of $20\text{cm}$ from the mirror. The focal length of mirror is

A U-tube with both end open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10mm$ above the water level on the other side. Meanwhile the water rises by $65mm$ from its original level (see diagram). The density of the oil is

A standing wave of amplitude $a,$ wavelength $\lambda$ and frequency $f$ is oscillating on a stretched string. The maximum speed at any point on the string is $\frac{v}{10}$, where $v$ is the speed of propagation of the wave. If $a={10}^{-3}\text{m}$ and $v=10{\text{ms}}^{-1}$, then $\lambda$ and $f$ are given by

A wheel is rotating with an angular speed $20\text{rad/sec}$. It is brought to rest by applying constant torque in $5\text{sec}$. If the moment of inertia of the wheel about the axis is $0.1{\text{kgm}}^2$, then the work done by the torque in $2\text{sec}$ is

A spherical black body of radius 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be

Find the electrostatic energy stored in a cylindrical shell of length $l$ , inner radius $a$ and outer radius $b$, co-axial with a uniformly charged wire with linear charge density $\lambda$,



$[k=\frac{1}{4\pi {\epsilon }_0}]$

Read each statement below carefully and state with reasons and examples, if it is true or false;
A particle in one-dimensional motion
a) with zero speed at an instant may have non-zero acceleration at that instant
b) with zero speed may have non-zero velocity,
c) with constant speed must have zero acceleration,
d) with positive value of acceleration must be speeding up.