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A motorcycle is going on an over-bridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over-bridge, the normal force on it

Three identical particles each of mass $1\text{kg}$ are placed with their centres on a straight line. Their centres are marked at $A,B$ and$C$ respectively. All the centres $A,B$ and $C$ are placed at equal distance of $2\text{m}$. Find the distance of centre of mass of system from $A$

An object is said to be in a state of free fall when

A charge of $3.14\times {10}^{-6}\text{C}$ is distributed uniformly over a circular ring of radius $20\text{cm}$. The ring rotates about its axis with angular velocity of $60\text{rad/s}$. Find the ratio of electric field to the magnetic field at a point on the axis located at a distance of $5\text{cm}$ from centre.

A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.

A particle moves on a rough horizontal ground with some initial velocity say $v_0$. If ${\frac{3}{4}}^{th}$ of its kinetic energy is lost overcoming friction in time $t_0$. Then, coefficient of friction between the particle and the ground is -

Displacement time graph of particle performing $SHM$ is shown in figure. Assume that mean position is at $x=0$, then kinetic energy and potential energy will be equal at:

[$T$ is time period and $A$ is amplitude]

Question 3

Light is falling on surfaces $S_1,S_2,and{S}_3$ as shown in the figure.









Surfaces on which the angle of incidence is equal to the angle of reflection is/are

(a) Only $S_1$

(b) $S_{1}and{S}_2$

(c) $S_{2}and{S}_3$

(d) All the three surfaces

Two magnetically uncoupled inductive coils have Q factors $q_1$ and $q_2$ at the chosen operating frequency. Their respective resistances are $R_1$ and $R_2$. When connected in series, the effective Q factor of the series combination at the same operating frequency is

The figure shows an area, $A=0.5{\text{m}}^2$ in a uniform magnetic field, $B=2.0\text{T}$ and making an angle of ${60}^{\circ }$ with the magnetic field. The value of the magnetic flux through the area is

Three vectors $\overrightarrow{A},\overrightarrow{B}and\overrightarrow{C}$ are related as $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$. If $\overrightarrow{C}$ is perpendicular to $\overrightarrow{A}$ and the $|\overrightarrow{C}|$ is equal to the $|\overrightarrow{A}|$, what will be the angle between $\overrightarrow{A}and\overrightarrow{B}$?

A fly wheel is in the form of a uniform circular disc of radius $1\text{m}$ and mass $2\text{kg}$. The work which must be done on it to increase its frequency of rotation from $5\text{rev/s}$ to $10\text{rev/s}$ is approximately

If the tension and diameter of a sonometer wire of fundamental frequency $n$ are doubled and density is halved, then its fundamental frequency will become

1. 9.25

A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4A_0$ in $4\text{s}$. The magnitude of this torque is

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation $I=I_{0}sin\omega t$, where $I_0=10Aand\omega =100\pi radian/sec$. The maximum value of e.m.f. in the second coil is

For sound waves, the
Doppler formula for frequency shift differs slightly between the two
situations: (i) source at rest; observer moving, and (ii) source
moving; observer at rest. The exact Doppler formulas for the case of
light waves in vacuum are, however, strictly identical for these
situations. Explain why this should be so. Would you expect the
formulas to be strictly identical for the two situations in case of
light travelling in a medium?

If light ray is incident at $i={90}^{\circ },$ find minimum value of prism angle in degrees for which emergence is not possible.

A force of $5N$ acts on a particle along a direction making an angle of $60°$ with vertical. Its vertical component will be

A wave is represented by the equation

y = (0.001 mm) sin[(50 $s^{-1}$)t + (2.0 $m^{-1}$)x].

1. 2

Three copper wires of length and cross-sectional area are $(l,A)$, $(2l,\frac{A}{2})$ and $(\frac{l}{2},2A)$ and their resistance are $R_1,R_2$ and $R_3$ respectively. The increasing order of resistances is-

The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as radius. When the radius is $1\text{cm},$ the altitude is $6\text{cm}.$ When the radius is $6\text{cm},$ the volume is increasing at the rate of $1\text{cu. cm/sec}.$ When the radius is $36\text{cm},$ then the rate of increase of the volume $\left(\text{in cu. cm/sec}\right)$ is

A container filled with viscous liquid is moving vertically downward with constant speed $3v_o$. At the instant shown, a sphere of radius $r$ is moving downward in the liquid with speed $v_o.$ The coefficient of viscosity is $\eta$. There is no relative motion between the liquid and the container. At the shown instant, the magnitude of viscous force on the sphere is

A long straight solenoid of cross-sectional diameter $d$ and with $n$ turns per unit of its length has a round loop of copper wire of cross-sectional area $A$ and resistivity $\rho$. The loop is lying at the centre of the solenoid, with its axis parallel to the axis of the solenoid. Find the current flowing in the loop if the current in the solenoid winding is increased with rate $I\text{Ampere/sec}$. The diameter of the loop is equal to the diameter of the solenoid.

A body is moving on a circle of radius of 80 m with a speed 20 m/s which is decreasing at the rate of 5 m/$s^2$ at an instant. The angle made by its acceleration with its velocity is

What is the speed of mass $100\text{g}$ having kinetic energy of $20\text{J}$?

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time;

A body of mass $m$ is launched up a rough inclined plane of angle ${45}^{\circ }$ with the horizontal. If the time of ascent is half the time of descent in covering the same distance, the coefficient of friction is