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What is the speed of sound in vacuum?

Velocity of a particle is in negative direction with constant acceleration in positive direction. Then match the following.
$\begin{array}{cc}\text{Table-1}& \text{Table-2}\\ \text{(A) Velocity - time graph}& \text{(P) Slope}\to \text{negative}\\ \text{(B) Acceleration - time graph}& \text{(Q) Slope}\to \text{positive}\\ \text{(C) Displacement - time graph}& \text{(R) Slope}\to \text{zero}\\ & \text{(S)}|\text{Slope}|\to \text{increasing}\\ & \text{(T)}|\text{Slope}|\to \text{decreasing}\\ & \text{(U)}|\text{Slope}|\to \text{constant}\end{array}$

A solid sphere of radius R is lying on a horizontal smooth surface. The sphere is hit by stick held horizontally at a height of $\frac{R}{2}$ above the center. The sphere moves forward with a velocity $v_0$ and angular velocity ${\omega }_0$ about its center. Then ${\omega }_0$ =

A simple harmonic wave of amplitude 2 units is travelling along positive x – axis. At a given instant,displacement for two different particles on the wave are 1 unit and $\sqrt{2}$ unit. If the wavelength of wave is $\lambda$, find the distance between them.

From a uniform circular disc of radius $R$ and mass $9M,$ a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is

A particle starts from mean position $x=0$ and starts moving towards negative extreme position. Find the initial phase constant $\varphi$ of the particle.

A $0.098\text{kg}$ block slides down a frictionless track as shown (Assume no energy loss on the entire track)
The time taken by the block to move from A to C is

A child is sitting on a swing whose minimum and maximum heights from the ground are $0.75\text{m}$ and $2\text{m}$ respectively. Its maximum speed will be

A wave travelling along a string is described by $y(x,t)=0.008\sin (85x-4t)$ in $\text{SI}$ units, where $x$ is in metres and $t$ is in seconds . Calculate the wavelength and frequency of the wave.

A container filled with a viscous liquid is moving vertically downwards with a constant speed $3v_0$. At the instant shown, a sphere of radius $r$ is moving vertically downwards (in liquid) has speed $v_0$. There is no relative motion between fluid and container. The coefficient of viscosity is $\eta$. Then at the shown instant, the magnitude of viscous force acting on sphere is

In the arrangement shown in figure, the string is light and inextensible and friction is absent everywhere. Find the speed of both the blocks after the block $\text{A}$ has ascended a height of $1\text{m}$. Given that $m_A=1\text{kg}$ and $m_B=2\text{kg}$. (Take $g=10{\text{m/s}}^2$)

A stone dropped from a building of height $h$ and it reaches the ground after $t$ seconds. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity $u$ and they reach the ground after $t_1$ and $t_2$ seconds respectively, then

AB is an L shaped obstacle fixed on a horizontal smooth table. A ball strikes it at A, gets deflected and restrikes it at B. If the velocity vector before collision is $\overline{v}$ and coefficient of restitution of each collision is ‘e’, then the velocity of ball after its second collision at B is (Neglect friction between contact surfaces and neglect the gravitational effect.)

A $6\text{V}$ battery of negligible internal resistance is connected across a uniform wire of length $1\text{m}$. The positive terminal of another battery of emf $4\text{V}$ and internal resistance $1\Omega$ is joined to the point $A$ as shown in figure. The ammeter shows zero deflection when the jockey touches the wire at the point $C$. The length of $AC$ is equal to:

The current through the $8\Omega$ resistor is (in Ampere) .

The equation of a standing wave in a stretched string is given by $y=5\sin \left(\frac{\pi x}{3}\right)\cos \left(40\pi t\right)$, where $x$ and $y$ are in $\text{cm}$ and $t$ is in $\text{sec}$. The separation between two consecutive nodes is (in $\text{cm}$)

When a wire of uniform cross-section a, length l and resistance R is bent into a complete circle, resistance between any two of diametrically opposite points will be

A galvanometer together with an unknown resistance in series is connected across two identical batteries each of 1.5 V. When the batteries are connected in series, the galvanometer records a current of 1 A, and when the batteries are in parallel, the current is 0.6 A. What is the internal resistance of the battery?

Two men of mass $60\text{kg}$ and $80\text{kg}$ stand on a plank of mass $20\text{kg}$. Both of them can jump with a velocity of $1\text{m/s}$ relative to the plank. In each event shown in column-I, find the velocity of plank after the event.

$\begin{array}{cccc}& \text{Column -I}& & \text{Column-II}\\ \text{(A)}& \text{Ram alone jumps to the left}& \text{(P)}& -\frac{17}{40}\text{m/s}\\ \text{(B)}& \text{Shyam alone jumps to the right}& \text{(Q)}& -\frac{1}{2}\text{m/s}\\ \text{(C)}& \text{Ram jumps to left and Shyam jumps to right simultaneously}& \text{(R)}& \frac{3}{8}\text{m/s}\\ \text{(D)}& \text{Ram jumps to left and after that Shyam jumps to right}& \text{(S)}& -\frac{1}{8}\text{m/s}\end{array}$
Which of the following is the only CORRECT combination ?

A disc which is at rest started to spin about a stationary axis. The angular acceleration of the disc is given by $\alpha =2\theta rad/s$, where $\theta$ is the angle of rotation of disc from its initial position. Which of the following graphs correctly represents the variation of angular velocity with respect to '$\theta$' ?

The focal length of a concave mirror is f and the distance from the object to the principal focus is x. The ratio of the size of the image to the size of the object is

With what acceleration ${}^{\prime }{a}^{\prime }$ shown, the elevator descends so that the block of mass $M$ exerts a force of $\frac{Mg}{10}$ on the weighing machine? [$g$ = acceleration due to gravity]

Derive an expression for the effective resistance of three resistances in series.

A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency $\frac{9}{\pi }rps$. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes ${37}^{\circ }$, the speed of the spot (a point) on the wall is

Two bodies performing $\text{S.H.M}$. have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them is

Two identical short bar magnets, each having magnetic moment M, are placed a distance of 2d apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

A stone is dropped from 25th storey of a multistoried building and it reaches the ground in 5s. In the first second it passes through how many storeys of the building?

$(g=10m/s^2)$

A parallel plate capacitor is to be constructed which can store $q=10\mu \text{C}$ charge at $V=1000$ Volt . The minimum plate area of the capacitor is required to be $A_1$ when space between the plates has air. If a dielectric of constant $k=3$ is used between the plates, the minimum area required to make such a capacitor is $A_2$. The breakdown field for the dielectric is $8$ times that of air. Then $\frac{A_1}{A_2}$ is:

A coil of inductance 8.4 mH and resistance $6\Omega$ is connected to a 12V battery. The current in the coil is 1.0A at approximately the time

A body of mass $4\text{kg}$ moving with a speed of $6\text{m/s}$ collides with another body of mass $8\text{kg}$ at rest. The lighter body comes to rest immediately after the collision. Find the coefficient of restitution $\left(e\right)$ for the collision.

A ball is thrown vertically downwards from a tower of height $60\text{m}$ with a speed of $20\text{m/s}$. The $y\text{(m)}-t$ curve of the ball is
[Take $g=10{\text{m/s}}^2$, consider point of projection as origin and upward displacement as positive]

An iron ball of mass $m=50\text{gm}$ falls from a height of $h_1=5\text{m}$ and rises upto $h_2=3.2\text{m}$ after colliding with the horizontal surface. If the time of contact with the surface is $\Delta t=0.02\text{s},$ find the average contact force$\left(\text{Newtons}\right)$ exerted on the ball by the horizontal surface. Take $g=10{\text{m/s}}^2$.

Rate of increment of energy in an inductor with time, in series LR circuit getting charge with battery of e.m.f. $E$ is best represented by [inductor has initially zero current]-

A circular ring of mass M and radius R is placed in a gravity free space. A small particle of mass m is placed on the axis of ring at a distance $\sqrt{3}$R from the centre of the ring. If particle and ring are released from rest. Speed with which particle passes through the centre of the ring is

A ball of mass $20\text{kg}$ is suspended from a massless string of length $5\text{m}$ as shown in figure. A bullet of mass $5\text{kg}$ moving with velocity $v_0\text{m/s}$ collides with the ball and sticks to it. Find the minimum value of $v_0$ so that the combined mass completes the vertical circular motion. [Take $g=10{\text{m/s}}^2$]

A particle moves in a circle of radius $10cm$ with a constant speed and time period of $0.2\pi s$. The acceleration of the particle is

A heavy box is slid across a rough floor with an initial speed of 4m/s. It stops moving after 8 seconds. If the average resisting force of friction is 10N, the mass of the box (in kg)is?

A thin spherical shell of mass M and radius R has a small hole. A particle of mass m is released at the mouth of the hole. Then

When we wear rubber slippers the charge remains for a longer time in our body still we feel less shock . why

We know that it is the electrons that move, so how is the potential defined as the work done to bring a POSITIVE CHARGE from infinity to a point?

An armored car $2\text{m}$ long and $3\text{m}$ wide is moving at $10\text{m/s}$ when a bullet hits it in a direction making an angle ${\tan }^{-1}\left(\frac{3}{4}\right)$ with the car as seen from the street. The bullet enters one corner of the car and passes out of the diagonally opposite corner. Neglecting any interaction between the bullet and the car, find the time for bullet to cross through the car.

Who sits with C?