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A wind with speed $40\text{m/s}$ blows parallel to the roof of a house. The area of the roof is $250{\text{m}}^2$. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho }_{air}=1.2{\text{kg/m}}^3)$.

A wheel starting from rest, rotates with $5{\text{rad/s}}^2$ angular acceleration along its axis. After $2\text{s}$ of motion, the magnitude of radial and tangential component of acceleration of the particle at a distance $2\text{cm}$ from the axis are ________ and ________ ${\text{cm s}}^{-2}$.

The threshold wavelength for a metal having work function $W_0$ is ${\lambda }_0$. What is the threshold wavelength for a metal whose work function is $\frac{W_0}{2}$?

If the velocity of water layers in river is given by $v=k{y}^2$, where $y$ is the height from the river bed. The force required to keep a square plate of area $A$ with constant velocity at height $h$ is $[\eta$ = coefficient of viscosity]

How can we define an ampere using the concept of the force between two infinitely long parallel current carrying conductors?

For the reaction, $S{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\rightleftharpoons S{O}_3\left(g\right)$ if $K_c=K_p(RT{)}^x$ where, the symbols have their usual meaning, then the value of $x$ is: (assuming ideality)

A vessel of $831\text{cc}$ contains ${}_1{\text{H}}^3$ at $0.6\text{atm}$ and $27{}^{\circ }\text{C}$. If the half life of ${}_1{\text{H}}^3$ is $12.3\text{years}$, then the activity of the gas is

A mass m is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be

A swimmer can swim with a speed $v$ in still water.


If the speed of the river flow is $u$ and the time taken by swimmer to reach opposite point on other bank in river is $T_1$ and the time taken to travel an equal distance upstream (against the water current) in the river is $T_2$, then ratio $\frac{T_2}{T_1}$ will have a value

The kinetic energy of a particle moving along a circle of radius $R$ depends on distance $\left(s\right)$ as $K=A{s}^2$ where $A$ is a constant.

The tangential force acting on the particle is

Two coherent sources of equal intensities produces, intensity maximum of $100$ units. If the amplitude of one of the sources is reduced by $20\%.$ The new maximum intensity produced will be-

A small block of mass $m=2kg$ is projected on a larger block of $20kg$ and of length $20\text{metres}$, with a velocity of $vm/s$ as shown in the figure. The coefficient of friction between the two blocks is $1.2$, while between the lower block and ground is $0.1$. The time taken by the small block to fall off the larger block is (Take $g=10m/s^2$)

Consider
the D−T reaction (deuterium−tritium fusion)

(a)
Calculate the energy released in MeV
in this reaction from the data:

=
2.014102 u

=
3.016049 u

(b)Consider
the radius of both deuterium and tritium to be approximately 2.0 fm.
What is the kinetic energy needed to overcome the coulomb repulsion
between the two nuclei? To what temperature must the gas be heated to
initiate the reaction? (Hint: Kinetic energy required for one fusion
event =average thermal kinetic energy available with the interacting
particles = 2(3kT/2);
k =
Boltzman’s constant, T =
absolute temperature.)

A uniformly charged rod (with total charge Q) and length l applies a force on other charge Q¹placed on its axis (i.e. along the rod) at a distance 1000l from its centre can be approximated as $\frac{KQ{Q}^1}{(1000l{)}^2}$ The reason it came out to be so is because

An airplane flying at a height of $1960\text{m}$ from the ground with constant horizontal velocity of $600\text{km/h}$ releases a bomb to hit a target on the ground. The time of flight and range of the bomb respectively are

Two charge +q and -q are situated at a certain distance. At the point exactly midway between them

As given in the figure two blocks $A$ & $B$ of weight $20\text{N}$ and $100\text{N}$ respectively are in equilibrium. These are being pressed against a wall by force $F$ as shown. If the coefficient of friction between the two blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by wall on block $B$ is $\left(f_2\right)$ and the frictional force applied by block $B$ on block $A$ is $\left(f_1\right)$.

A light ray is incident normally on the face $AB$ of a right-angled glass prism $ABC(\mu =1.50)$ as shown in figure. What is the largest angle $\varphi$ for which the light ray is totally reflected at the surface $AC$ ?

A $40\text{kg}$ slab rests on a frictionless floor. A $10\text{kg}$ block rests on top of the slab. The static coefficient of friction between the block and the slab is 0.60 while the kinetic coefficient of friction is 0.40. The $10\text{kg}$ block is acted upon by a horizontal force of $100\text{N}$ . The resulting acceleration of the slab will be

At time t =0, a rock climber accidentally allows a piton (metal spike) to fall freely from a high point on the rock wall to the valley below him. Then, after a short delay, his climbing partner, who is 10 m higher on the wall, throws a piton downward. The positions 'y' of the pitons versus 't' during the falling are given in figure. With what speed is the second piton was thrown?

A long cylindrical iron core of cross-sectional area $5.00{\text{cm}}^2$ is inserted into a long solenoid having $2000\text{turns/m}$ and carrying a current $2\text{A}$. The magnetic field inside the core is found to be $1.57\text{T}$. Neglecting the end effects, find the magnetization $I$ of the core and the pole strength developed

An iron rod of length $50\text{cm}$ is joined at an end to an aluminium rod of equal length to form a system. All measurements refer to ${20}^{\circ }C$. If coefficient of linear expension of iron and aluminium are $12\times {{10}^{-6}}^{\circ }C$ and $24\times {{10}^{-6}}^{\circ }C$ respectively, find average coefficient of linear expension of composite system?

Figure (16-E7) shows two coherent sources $S_1$ and $S_2$ which emit sound of wavelength X in phase. The separation between the sources is $3\lambda$. A circular wire °f large radius is placed in such a way that $S_1,S_2$ lies in its plane and the middle point of $S_1,S_2$ is at the centre of the wire. Find the angular positions $\theta$ on the wire for which constructive interference takes place.

A convex mirror of focal length ${}^{\prime }{f}^{\prime }$ is placed at the origin with its reflecting surface towards the negative $x-axis$. Choose the correct graphs between ${}^{\prime }{v}^{\prime }$ and ${}^{\prime }{u}^{\prime }$ for $u<0$.

I have a container that is 20cm tall and filled fully with water. The lift accelerates up at 10 $\text{m}/{\text{s}}^2$. What is the pressure difference between the top surface of the water and the bottom of the container(in pascal)? Take density of water as 1kg/lit.

The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.

A boy throws up a ball in a stationary lift and the ball returns to his hands in 10 s. Now if the lift starts moving up at a speed of 5 m/s. The time taken for a ball thrown straight up to return to his hands is:

Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi }{2}$ at point $A$ and $2\pi$ at point $B$. Then the difference between the resultant intensities at $B$ and $A$ will be

Two point charges $+10\text{nC}$ and $-10\text{nC}$ are separated by a distance of $6\text{cm}$. Find the electric flux hrough a circle of radius $4\text{cm}$ placed with its centre coinciding with the mid - point of line joining the two charges in the perpendicular plane as shown in the figure.

Infinite no.of bodies, each of mass 3kg are situated at distances 1m, 2m, 4m, 8m....... respectively on x-axis. The resultant intensity of gravitational field at the origin will be

Find potential difference $V_{AB}$ between two points $\text{A}$ and $\text{B}$ whose position vectors are $r_A=(\hat{i}-2\hat{j}+\hat{k})\text{m}$ and $r_B=(2\hat{i}+\hat{j}-2\hat{k})\text{m}$, in an uniform electric field $E=(2\hat{i}+3\hat{j}+4\hat{k})\text{N/C}$.

In the above problem, given that $M_2=2M_1$ and the tension in the string is T.If the positions of the masses are reversed, the tension in the string will be

When a satellite in a circular orbit around the earth enters the atmospheric region, it encounters small air resistance to its motion. Then -

In uniform circular motion