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Four point masses, each of value $m$, are placed at the corners of a square ABCD of side $l$. The moment of inertia of this system about an axis passing through A and parallel to BD is

A block of mass $M$ is attached to a horizontal spring and is executing SHM, with amplitude $A_1$. When the mass $M$ passes through its mean position, a smaller mass $m$ is placed over it gently and both of them move together with amplitude $A_2$. The ratio of $\left(\frac{A_1}{A_2}\right)$ is

Two points $A$ and $B$ on a disc have velocities $v_1$ and $v_2$ at some moment. Their directions make angles ${60}^o$ and ${30}^o$ respectively with the line of separation as shown in the figure. The angular velocity of the disc is:

Which one of the following graphs represent the velocity of a steel ball which falls from a height on to a marble floor?

An Indian rubber cord $L\text{m}$ long and area of cross-section $A{\text{m}}^2$ is suspended vertically. Density of rubber is $D{\text{kg/m}}^3$ and Young's modulus of rubber is $E{\text{N/m}}^3.$ If the wire extends by $l\text{m}$ under its own weight, then extension $l$ is

There are four concentric shells A, B, C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges +q and –q respectively. Shell C is now earthed. The potential difference $V_A-V_C$ is :

The similarity between the sound waves and light waves is

[KCET 1994]

A force $F$ acting on a particle depends on displacement as $F\propto x^n$. Then, power delivered by the force depends on $x$ as:

The mass of Mr x is 50kg and the uncertainty in measurement is 1 kg.The mass of Mr y is 55kg and the uncertainty in measurement is 2 kg. Find the difference of their masses with correct uncertainties.

Assuming frictionless contact everywhere, determine the magnitude of external horizontal force $P$ applied at the lower end for equilibrium of the rod as shown in figure. The rod is uniform and its mass is ${}^{\prime }{m}^{\prime }$.

A particle is projected vertically upwards with speed $20\text{m/s}$ from top of a tower of height $20\text{m}$ as shown in figure. Given $B$ is top most point of trajectory and $C$ is at same height as $A$.

List-I gives certain statements regarding particle

List - II gives corresponding results in SI units.

Match the statements in List-I with corresponding results in List-II.



$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(I)}& \text{ratio of maximum height from ground (BD)}& \text{(P)}& \frac{1}{\sqrt{2}}\\ & \text{to the initial height from ground (AD) is}& & \\ \text{(II)}& \text{ratio of distance travelled in 1}{}^{st}\text{second to}& \text{(Q)}& 1\\ & \text{the distance travelled in 2}{}^{nd}\text{second is}& & \\ \text{(III)}& \text{ratio of initial speed at A to the final}& \text{(R)}& 2\\ & \text{just before reaching to ground (D) is}& & \\ \text{(IV)}& \text{ratio of time taken from A to C and time}& \text{(S)}& 3\\ & \text{taken from A to B is}& & \end{array}$

Given a particle's velocity- time graph which is in motion along a line. What is the total distance travelled by the particle till t = 20 sec?

Steady flow is also called?

A locomotive of mass $m$ starts moving so that its velocity varies as $v=\alpha s^{2/3}$, where $\alpha$ is a constant and $s$ is the distance traversed. The total work done by all the forces acting on the locomotive during the first $t$ second after the start of motion is

A car is moving with constant speed on a road as shown in figure. The normal reaction by the road on the car is $N_A,N_B$ and $N_C$ when it is at the points A, B and C respectively. Then:

A projectile rises upto a maximum distance of $\frac{R}{1-k^2}$ where K is a constant and R is the radius of Earth. If the velocity of the projectile with which it should be fired upwards from the surface of Earth to reach this height is equal to the product of a coefficient and escape velocity, then this coefficient is equal to:

Two blocks of mass $m_1=2\text{kg},m_2=4\text{kg}$ connected by weightless spring of stiffness $k$ rest on a horizontal plane as shown. $m_2$ is shifted a small distance $x=1\text{cm}$ to the left and then released. Find the velocity of COM of the system just after $m_1$ break off the wall. Assume $k=4\text{N/m}$.

A spinning top has an angular retardation of $\alpha =k{\omega }^2$ (in ${\text{rad/s}}^2$), where $\omega$ is angular velocity of the top and $k=1{\text{rad}}^{-1}$. At ${\theta }_0=0\text{rad}$, if ${\omega }_0=120\text{rad/s}$, then the relation between angular displacement ($\theta$) and angular velocity is

Find the integration of $\int \frac{e^{{\sin }^{-1}x}}{\sqrt{1-x^2}}.dx$

Vector A has magnitude of 5 units and makes an angle of ${30}^{\circ }$ with the x-axis. Vector B has magnitude 10 units & make an angle of ${60}^{\circ }$ with the x-axis. Find $\overrightarrow{A}+\overrightarrow{B}$

A scooterist is approaching a circular turn of radius $80\text{m}$. He reduced his speed from $27{\text{kmh}}^{-1}$ at constant rate of ${\text{0.5 ms}}^{-2}$. Find net acceleration and angle made by it wrt tangential deceleration

Figure shows the position-time $(x-t)$ graph of one dimensional motion of a body of mass $500\text{g}$. What is the time interval between two-consecutive impulses received by the body?

The time taken by an engine of power $10\text{kW}$ to lift a mass of $200\text{kg}$ to a height of $40\text{m}$ is $(g=10m{s}^{-2})$

Find derivative of $f\left(x\right)=x+\frac{1}{x}+1$

At some instant $\overrightarrow{v}=4\hat{i}-3\hat{j}\text{m/s}$ and $\overrightarrow{a}=2\hat{i}+\hat{j}{\text{m/s}}^2$. Find the radius of curvature at that instant.

An uniform rod of density $\rho$ is placed in a wide tank containing a liquid of density ${\rho }_0({\rho }_0>\rho )$. The depth of the liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position, the rod makes an angle $\theta$ with the horizontal. Then, identify the correct relation :

The position of the particle is given by $x\left(t\right)=(4t^2-3t+2t^3)$, its acceleration will be

Find the force of interaction between $2kg$ and $3kg$. (Assume all surface are smooth)

Four students were doing the photoelectric experiment with lights having different wavelengths and intensities.

$\begin{array}{ccc}Name& Wavelength\left(nm\right)& intensity\left(w/m^2\right)\\ RAM& 263& 20\\ SATRA& 544& 120\\ AVINASH& 674& 120\\ HIMANSHU& 372& 65\end{array}$

If these four students are strong supporters of the classical wave model of light, then whose experiment will supposedly need the highest stopping potential?

A shell of mass $M$ and radius $R$ has a point mass $m$ placed at a distance $r$ from its centre. The gravitational potential energy $U\left(r\right)$ vs $r$ will be

The Van Der Waal’s equation of state for some gases can be expressed as: $(P+\frac{a}{V^2})(V-b)=RT$ Where $P$ is the pressure, $V$ is the molar volume and $T$ is the absolute temperature of the given sample of gas and $a,b$ and $R$ are constants.



The dimensions of constant $b$ are

Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire1

When forward bias is applied to a p-n junction, then what happens to the potential barrier $V_B$, and the width of charge depletion region?

A closed tube filled with water is rotating as shown in figure. The pressure difference $P_A-P_C$ is

The initial velocity of the particle is $10\text{m/sec}$ and its retardation is $2{\text{m/sec}}^2$. The distance moved by the particle in $5^{\text{th}}$ second of its motion is

A cube has sides of length L = 0.300 𝑚. It is placed with one corner at the origin as shown in the

figure. The electric field is not uniform, but it is given by $\overrightarrow{E}=(-5.00N{C}^{-1})x\hat{i}+\left(3.00N{C}^{-1}\right)z\hat{k}$.

The total electric charge inside the cube is

A body of mass 1 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{4}$ of its original velocity. The mass of the second body is

A block of mass $2.0\text{kg}$ is pulled up on a smooth incline of angle ${30}^{\circ }$ with the horizontal. If the block moves with an acceleration of $1.0{\text{m/s}}^2$, then the power delivered by the pulling force at a time $4.0\text{s}$ and the average power delivered during the $4.0\text{s}$ after the motion starts are

If $\alpha$ denotes the coefficient of linear expansion of a block , $L$ denotes length of the block and $T$ denotes temperature, then which one of the following options is true?

Which of the following results is true?

The angular speed of a fly wheel making 120 revolutions/minute is

Convert $\frac{\pi }{4}$ radians to degrees

Two charges of unknown magnitudes are kept 5m away from each other. The magnitude of force between them is measured to be F. If these charges are then moved so that the distance between them is 20m, what is the new force between them?

The quantity $\frac{pV}{kT}$ represents

A non-conducting square sheet of side 10 m is charged with a uniform surface charge density,$\sigma =-60\frac{\mu C}{m^2}$ . Find the magnitude and orientation of electric field vector due to the sheet at a point which is d = 0.02 mm away from the midpoint of the sheet.

A solid cylinder of mass $20\text{kg}$ rotates about its axis with an angular speed of $100\text{rad/s}$. The radius of the cylinder is $0.25\text{m}$. The kinetic energy associated with the rotation of the cylinder is

Three concentric spherical metallic shells A, B and C of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma ,$ respectively.

If shells A and C are at the same potential, the relation between the radii $a,b$ and $c$ is