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A sphere of mass $m$ is rolling on a frictionless surface (as shown in the figure) with a translation velocity $v\text{m/s}$. The sphere will climb on the inclined plane if $v$ is

Voltage multiplication factor is given by

What will be the angular momentum of an electron, in a hydrogen atom, if its energy is $1.5\text{eV}$?

The mass of hydrogen molecule is $3.32\times {10}^{-27}$ kg. If ${10}^{23}$ hydrogen molecules strike a fixed wall of area 2 $c{m}^2$ at an angle of ${45}^{\circ }$ to the normal and rebound elastically with a speed of 103 m/s. Calculate the pressure exerted on the wall.

The resultant of the two vectors having magnitude $2$ and $3$ is $1$. What will be their cross product?

1. 8.25

The apparent depth of water in a cylindrical water tank of diameter $2R\text{cm}$ is reducing at the rate of $x\text{cm/min}$ when water is being drained out at a constant rate. The actual amount of water drained in ${\text{cm}}^3\text{/min}$ is

$(n_1=$ refractive index of air, $n_2=$ refractive index of water$)$

Four rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about the axis yy' is

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift's motion is given in Column I and the distance where the water jet hits the floor of the lift is given in Column II. Match the statements from Column I with those in Column II and select the correct option using the code given below the lists.

$\begin{array}{cc}\text{Column~I}& \text{Column~II}\\ \text{(A) Lift is accelerating}& \text{1. d = 1.2 m}\\ \text{vertically up.}& \\ \text{(B) Lift is accelerating}& \text{2. d > 1.2 m}\\ \text{vertically down with}& \\ \text{an acceleration less}& \\ \text{than the gravitational}& \\ \text{acceleration.}& \\ \text{(C) Lift is moving}& \text{3. d < 1.2 m}\\ \text{vertically up with}& \\ \text{constant speed}.& \\ \text{(D) Lift is falling freely.}& \text{(4) No water leaks out of the jar}\end{array}$

A small disc is placed at the top of a hemisphere of radius R as shown in figure. What is the smallest velocity that should be given to the disc for it to leave the hemisphere and not slide down it?

The resultant of $\overrightarrow{P}$ and $\overrightarrow{Q}$ is perpendicular to $\overrightarrow{P}$. What is the angle between $\overrightarrow{P}and\overrightarrow{Q}$

The value of the integral $\underset{-\pi }{\overset{\pi }{\int }}\sin mx\cdot \sin nxdx,$ for $m\ne n(m,n\in I)$ is

A rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha -\beta t,$ at the time $t$, where $\alpha ,\beta$ are constants. The angle through which it rotates before it stops is

Find the path difference between the two rays, both originating from point $O$ and meeting at $P$, as shown in the figure.

Sides of a cube is made from $6$ identical sheets. If co-efficient of linear expansion of sheet is $\alpha$ and temperature is changed by $\Delta T$. Find the change in volume if side length of the cube is $a$.

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius, the orbital velocity will be

If Sameer moves from point $A$ having position vector $2\hat{i}+4\hat{j}+2\hat{k}$ to point $B$ having position vector $6\hat{i}+8\hat{j}+3\hat{k}$, what is his displacement vector?

The lens which detective uses to see the things larger or bigger, which is thicker in the middle and thinner at the edges. This type of lens is called _________.

If we express the energy of a photon in KeV and the wavelength in angstroms, then energy of a photon can be calculated from the relation

Tap on the bubbles with statements that give the result as 6.

An elelctric field $\overrightarrow{E}=50\hat{i}+75\hat{j}{\text{NC}}^{-1}$ exist in a certain region of space. Assume that the potential at the origin to be zero. The potential at a point $\text{P}$$(1\text{m},2\text{m})$will be

A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in Fig. 25.25. An electric field is induced

Eight drops of water, each of radius 2 mm are falling through air at a terminal velocity of $8cm{s}^{-1}$. If they coalesce to form a single drop, then the terminal velocity of combined drop will be

The three rods shown in the figure have identical dimensions. Heat flows from the hot end at a rate of $40\text{W}$ in the arrangement (a). Find the rate of heat flow when the rods are joined as in the arrangement shown in (b).
[Assume $K_{AI}=200{\text{W/m}}^{\circ }\text{C}$ and $K_{cu}=400{\text{W/m}}^{\circ }\text{C}$]

A ball of mass m moving with a velocity u rebounds from a wall. The collision is assumed to be elastic and the force of interaction between the ball and wall varies as shown in fig. then the value of $F_0$ is

Three
girls skating on a circular ice ground of radius 200 m start from a
point Pon the
edge of the ground and reach a point Qdiametrically
opposite to Pfollowing
different paths as shown in Fig. 4.20. What is the magnitude of the
displacement vector for each? For which girl is this equal to the
actual length of the path skated?

A sample of four hydrogen atoms, all in the $n^{th}$ excited state, de- excite to the ground state, and shows a maximum of six different spectral lines. Hence the value of $n$ is:

Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures?

The wire $\text{PQ}$ has mass $0.5\text{kg}$ and resistance $2\Omega$ can slide on the smooth, very long horizontal parallel rails separated by a distance of $1\text{m}$. The resistance of the rails is negligible. A uniform magnetic field of magnitude $0.6\text{T}$ exists in the rectangular region, and a resistance $3\Omega$ connects the rails outside the field region. At $t=0$, the wire $\text{PQ}$ is pushed towards the right with a speed $v=5\text{m/s}$. Find the current in the loop at an instant when the speed of the wire $\text{PQ}$ is $5\text{m/s}$.

Question 15



Does force of gravity act on dust particles?

A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the phase difference between two displacements of a certain point on the wave, whose time difference is $0.002\text{s}$.

Locate the image of the point object O in the situation shown in the figure with respect to the pole $P$ of the spherical surface. The point C denotes the centre of curvature of the refracting surface.