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A metallic rod of length l is tied to a string of length 2l and made to rotate angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the emf induced across the ends of the rod is

A ball of mass m moving with a velocity v undergoes an oblique elastic collision with another ball of the same mass m but at rest. After the collision, if the two balls move with the same speeds, the angle between their directions of motion will be

The distance and displacement covered respectively by a particle after half a revolution of circular path of radius $r$ are

1. 196.32

Two forks $A$ and $B$ produce 3 $\text{beats/s}$. Forks $B$ and $C$ produce 5 $\text{beats/s}$. $A$ and $C$ will produce

If y=ln⁡x ,then $\frac{dy}{dx}$ will be

If the tangent at any point $P(4m^2,8m^3)$ on the curve $x^3-y^2=0$ is a normal to itself at another point $Q,$ then the value(s) of $m$ is/are

The operating temperature of a tungsten filament in an incandescent lamp is $2000\text{K}$ and its emissivity is $0.3$. Find the surface area of the filament of a $25\text{watt}$ lamp.

Stefen's constant $\sigma =5.67\times {10}^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$

Two satellites of same mass $m$ are launched in the same orbit (radius $r$) around the earth (mass $M$) so as to rotate opposite to each other. If they collide inelastically and stick together as wreakage, the total energy of the system just after collision is-

Find the slope of the graph shown in the figure.





Where:

$V_s\to$ stopping potential $\left(\text{V}\right)$

$f\to$ frequency of the incident radiation $\left(\text{Hz}\right)$

A mild steel rod tapers uniformly from $24mm$ dia to $12mm$ dia over its length of $400mm$. The rod when held vertical is subjected to an axial tensile load of $12kN$. $E=2\times {10}^{5}N/m{m}^2.$ The extension of the rod in $mm$ would be

Two particles having mass ratio n : 1 are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is :

A square loop of side $l$ enters a region of transverse magnetic field with a constant speed $v$ as shown in the figure. The resistance of the loop is $r$. Choose the graph that represents the variation of induced current $\left(i\right)$ across the loop versus time. [Given, $d>2l$]

The sum and the product of the quadratic equation $(x-\sqrt{2})(x+\sqrt{8})=5$ are and respectively.

A block is released from point $\text{A}$ as shown in figure. All surfaces are smooth and there is no loss of mechanical energy anywhere. Find the time period of oscillations of block.

The torque required to keep a magnet of length $20\text{cm}$ at ${30}^{\circ }$ to a uniform magnetic field is $2\times {10}^{-5}\text{Nm}$. The magnetic force on each pole is-

Two vectors $\overrightarrow{X}$ and $\overrightarrow{Y}$ have equal magnitude. The magnitude of $(\overrightarrow{X}-\overrightarrow{Y})$ is $n$ times the magnitude of $(\overrightarrow{X}+\overrightarrow{Y})$. The angle between $\overrightarrow{X}$ and $\overrightarrow{Y}$ is:

Show that
is
perpendicular to,
for any two nonzero vectors

Figure 3.21 shows the x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0? If not, suggest a suitable physical context for this graph.

(Fig 3.21)

The image of a point source $\text{O}$ placed at the bottom of the container filled with water is formed at $I$ as shown in the figure. Find the focal length of the mirror.

Two parallel plate capacitors $\text{A}$ and $\text{B}$ having capacitance $2\mu \text{F}$ and $4\mu \text{F}$ are charged seprately upto $20\text{V}$ and $10\text{V}$ respectively. Now the positive plate of $\text{A}$ is connected to the positive plate of $\text{B}$. Similarly negative plate of $\text{A}$ is connected with negative plate of $\text{B}$. Find how much heat is produced in the circuit?

1. 2.4

When a horizontal force $P$ acts on a cart of mass $20\text{kg}$, it moves with a uniform velocity on a horizontal floor. When a force of $1.2P$ acts on the cart, it moves with an acceleration of $0.05{\text{m/s}}^2$. Find the value of $P$.

Which of these is true?

Time-velocity graph of a particle is shown in Fig.
(i) Calculate the distance travelled in first 8 seconds.

With what acceleration $a$ should the bigger box shown in the figure descend so that the block of mass $M$ exerts a force $\frac{Mg}{4}$ on the floor of the box?

(Hint:- Use the concept of pseudo-force)

The refracting angle of prism is A and refractive index of material of prism is cot $\frac{A}{2}$ The angle of minimum deviation is