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Two projectiles $A$ and $B$ are thrown simultaneously towards each other. If the initial distance between them is $30\text{m}$ and their initial velocities are $V_A=2\hat{i}-3\hat{j}$ and $V_B=5\hat{i}+\hat{j}$. Then the minimum distance between them during their flight will be.

A uniform rope of mass 0.1 kg and length 2.45 m hangs from the ceiling. Calculate the time taken by a transverse wave to travel the full length of the rope

In Newton's experiment of cooling, the water equivalent of two similar calorimeters is 10 gm each. They are filled with 350 gm of water and 300 gm of a liquid (equal volumes) separately. The time taken by water and liquid to cool from ${70}^{o}Cto{60}^{o}C$ is 3 min and 95 sec respectively. The specific heat of the liquid will be

Two blocks of masses $m_1$ and $m_2$ are connected by a weightless spring of stiffness $k$, rests on a smooth horizontal plane. Mass $m_2$ is shifted by a small distance $x_0$ to the left and released. The velocity of the center of mass of the system when $m_1$ breaks off the wall is,

1. 200

An isolated parallel plate capacitor of capacitance $C$ has four surfaces with charges $Q_1,Q_2,Q_3$ and $Q_4$ as shown in the figure below. The potential difference across plates is (In the given diagram, $Q_1$ and $Q_4$ are the charges on the outer surfaces of the left & right plates respectively)

Two bodies A and B of mases m and 2m respectively are placed on a smooth floor. They are connected by a spring. A third body C of mass m moves with velocity $v_0$ along the line joining A and B and collides elastically with A as shown in figure. At a certain instant of time $t_0$ after collision, it is found that the instantaneous velocities of A and B are the same. Further at this instant the compression of the spring is found to be $x_0$. Determine (a) the common velocity of A and B at time $t_0$ and (b) the spring constant.

The diagram shows an arrangement of identical metal plates placed parallel to each other and the variation of potential between the plates by dotted line. Using the details given in diagram, the equivalent capacitance connected across the battery is equal to
(Separation between the plates = L, area of each plate = A)

An object $O$ is moving with velocity of $(\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$ and a plane mirror in $yz$ plane facing the object is moving with velocity of $\left(2\hat{i}\right)\text{m/s}$. The velocity of the image with respect to ground (in SI units) will be

What was observed by Rutherford when electric current was passed through Uranium plates ?

Find the angle between the net acceleration vector and tangential acceleration vector for a particle moving in a circle of radius $4m$ and its speed is increasing at $3m/s$ every second, when the speed of the particle is $4m/s$.

A glass plate of thickness $t$ is placed in front of one of the slits in a Young's double slit experiment. It is found that the interference pattern is shifted through a distance $d$. If this whole setup is immersed in water, the shift in pattern will be:

$[\text{Given: Refractive index of glass,}{\mu }_g=\frac{3}{2},\text{Refractive index of water}{\mu }_w=\frac{4}{3}]$

In the figure shown below, if the downward acceleration $a$ of $B$ is along the fixed incline, then find the accleration of $A$ if $A$ and $B$ remains in contact.

Question 20

What is momentum? Write its SI unit. Interpret force in terms of momentum. Represent the following graphically



(a) momentum versus velocity when mass is fixed.

(b) momentum versus mass when velocity is constant

A hollow sphere of radius r rolls down a rough inclined plane of inclination ${30}^{\circ }$ with the horizontal. If it starts from rest at the top and reaches the bottom of the plane 2.5 m long, the velocity of the centre of the sphere is ( Take g = 10 m $s^2$ )

Monochromatic light of wavelength $640\text{nm}$ falls normally on a glass plate of refractive index $\mathrm{1.6.}$ The waves reflected from the upper and lower faces of the film will interfere constructively if the least thickness of the plate is .

1. 1.732

The point from where a ball of mass $2\text{kg}$ is projected is taken as the origin of the co-ordinate axes. The $x$ and $y$ components of its displacement are given by $x=6t$ and $y=8t-5t^2$. Find the change in its momentum ( in 𝒌𝒈 𝒎/𝒔) from $t=0$ to $t=2$ seconds.

A sphere of radius $R$ is in contact with a wedge. The point of contact is at a distance $\frac{R}{5}$ from the ground as shown in the figure. The wedge is moving with velocity $20\text{m/s}$ towards left, then the velocity $v$ of the sphere at this instant will be:

does magnetic field of solenoid depend upon radius?if it does why it is not included in the equation?

A horizontal uniform rod of mass ${}^{\prime }{m}^{\prime }$ has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass ${}^{\prime }{m}^{\prime }$ which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest.


The magnitude of normal reaction exerted by the rod on the cylinder is

Light is incident at an angle $i$ on one planar cross-sectional end of a transparent cylindrical rod of refractive index $\mu$. Find the minimum value of $\mu$, so that the light entering the rod does not emerge from the curved surface of the rod, irrespective of the value of $i$.

An ice cube of mass $0.1\text{kg}$ at $0^{\circ }\text{C}$ is placed in an isolated container which is at ${227}^{\circ }\text{C}$. The specific heat $S$ of the container varies with temperature $T$ according to the empirical relation $S=A+BT$, where $A=100\text{cal/kg K}$ and $B=2\times {10}^{-2}{\text{cal/kg K}}^2$. If the final temperature of the container (with the material in it) is ${27}^{\circ }\text{C}$, determine the mass of the container.
[Latent heat of fusion of water $=80{\text{cal/g}}^{\circ }\text{C}$, specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$]

When a 5 $V$ potential difference is applied across a wire of length $0.1m$, the drift speed of electrons is $2.5\times {10}^{-4}m{s}^{-1}$. If the electron density in the wire is $8\times {10}^{28}{m}^{-3}$, the resistivity of the material is close to:

For the stationary wave y= 4 sin( $\pi x$/15) cos(96 $\pi$ t) the distance between a node and the next antinode is

If Bohr’s
quantisation postulate (angular momentum = nh/2π)
is a basic law of nature, it should be equally valid for the case of
planetary motion also. Why then do we never speak of quantisation of
orbits of planets around the sun?

One mole of a monoatomic ideal gas is taken along two cyclic processes $E\to F\to G\to E$ and $E\to F\to H\to E$ as shown on given $P-V$ diagram.

The processes involved are purely isochoric, isobaric, isothermal or adiabatic.



Which of the following is/are correct ?