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Two trains move towards each other with the same speed. Speed of sound is $340{\text{ms}}^{-1}$. If the pitch of the tone of the whistle of one when heard on the other changes by $\frac{9}{8}$ times, then the speed of each train is:

An object is displaced from position vector $\overrightarrow{r_1}=(2\hat{i}+3\hat{j})$ $\text{m}$ to $\overrightarrow{r_2}=(4\hat{i}+6\hat{j})$$\text{m}$ under a force $\overrightarrow{F}=(3x^2\hat{i}+2y\hat{j})$ $\text{N}$. Find the work done.

A particle starts from the point $(0m,8m)$ and moves with uniform velocity of $3\hat{i}\text{m/s}$. After 5 seconds, the angular velocity of the particle about the origin will be :

Figure shows a transparent hemisphere of radius 3.0 cm made of a material of refractive index 2.0.

(a) A narrow beam of parallel rays is incident on the hemisphere as shown in the figure. Are the rays totally reflected at the plane surface ?

(b) Find the image formed by the refraction at the first surface.

(c) Find the image formed by the reflection or by the refraction at the plane surface.

(d) Trace qualitatively the final rays as they come out of the hemisphere.

A uniform solid sphere of mass 1 kg and radius 10 cm is kept stationary on a rough inclined plane by fixing a highly dense particle at B. Inclination of plane is ${37}^{\circ }$ with horizontal and AB is the diameter of the sphere which is parallel to the plane, as shown in figure. Calculate

(i) Mass of the particle fixed at B

A metre gauge train is moving at a speed of $36\text{km/hr}$ along a curved track of radius $10\sqrt{3}\text{m}$. Find the height of the outer rail with respect to the inner rail, so that there is no side pressure on the rails. Take $g=10{\text{m/s}}^2$ and the width of the track to be $1\text{m}$.

Find the extreme values of cos2x+cos2x

The phase difference between the displacement and acceleration of particle executing $\text{S.H.M.}$ $\left(\text{in radian}\right)$ is

The ratio of electric field due to an electric dipole at points situated at a distance r along its axial line and along its equatorial plane is

Why Avector.Bvector=abcosø and Avector×Bvector= absinø ?Explain.

If equivalent weight of a trivalent metal is 32.7. The molecular weight of its chloride is :

Electric flux is a _______ quantity

An ideal $C{O}_2$ gas obeys the law $P{V}^x=$ constant. The range of $x$ for which the gas has non-positive molar specific heat at normal temperature is

A wheel of radius $r=1\text{m}$ is rolling with an angular velocity $\omega =\frac{\pi }{3}\text{rad/s}$ about its center and velocity of its center of mass is $v_{com}=2\text{m/s}$. Point $P(0,0)$ is in contact with ground initially, find its height (in $\text{m}$) from the surface after time $t=1\text{s}$.

A point $P$ having the coordinate $(2,3)$. Find the position vector of $P$ ?

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are 20 cm and 40cm and they carry currents of 0.2A and 0.3A respectively in opposite directions. If ${\mu }_0$ is permeability of vacuum, then the magnetic field in$Wb/m^2$at the common centre is

What is a meta centre ?

A force of 98N is just able to move a block of mass 20kg on a rough horizontal surface.

1.Calculate the coeeficent of friction

and the angle

Approximate the gravitational force exerted on the moon by the earth and the sun. A) during a solar eclipse and B) during a lunar eclipse. Given the mass of sun = 2 x 10³⁰ kg mass of earth 6 x 10²⁴ kg mass of the moon 7.4 x 10²² kg radius of earth's orbit around the sun 1.5 x 10¹¹ m and radius of moon's orbit around the earth 3.8 x 10⁸ m.

A boat is moving due East in a region where the earth's magnetic field is 5×10^-5 T due north and horizontal . The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50m/s , what will be the magnitude of the induced emf in the wire of aerial !

A circular coil of radius r carries current I. If another circular coil of radius 2r carries the same current, then the ratio of the magnetic fields at the centers of the circular is

calculate the mass of photon with wavelength=3.6 armstrong

A uniform slab of dimension 10 cm $\times$ 10 cm $\times$ 1 cm is kept between two heat reservoirs at temperatures ${10}^{\circ }C$ and ${90}^{\circ }C$. The larger surface areas touch the reservoirs. The thermal conductivity of the material is $0.80W{m}^{-1\circ }{C}^{-1}$ Find the amount of heat flowing through the slab per minute.

A man walks on a straight road from his home to a market 2.5 km away with a speed of $5km{h}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5km{h}^{-1}$. What is the
a) magnitude of average velocity, and
b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min,
(iii) 0 to 40 min? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero!]

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

The speed of the particle around the circle is

A football player kicked a ball with a velocity of $20m{s}^{-1}$ in a direction making an angle of ${60}^{\circ }$ with horizontal. Find the velocity with which he should run in the same direction so that the ball remains above this head.

A wire of length 2.00 in is stretched to a tension of 160 N. If the fundamental frequency of vibration is 100 Hz, find its linear mass density.

Distinguish between policy and rule.

The two rails of a railway track, insulted from each other and from the ground, are connected to a milli volmeter. What will be the reading of the millivolt meter when a train travels on the track at a speed of $182km{h}^{-1}$ ? The vertical component of earth's magnetic field is $0.2\times {10}^{-4}$ T and the rails are seperated by 1 m

When tungsten put in the volcano, it will melt or not

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s²).

(The figures are schematic and not drawn to scale)

A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

Diamond sparkle because of

A satellite orbiting close to the surface of earth does not fall down because the gravitational force

If the ordinate (value of the '$y$' coordinate) is thrice the abscissa (value of the '$x$' coordinate), then find the point where $14x-3y=15$.

In Coolidge tube electrons were ejected by the cathode because of which method:

Trajectory of particle in a projectile motion is given as y = x - $\frac{x^2}{80}$ .

Here , x and y are in meters. For this projectile motion match the following with g = 10 m / $s^2$

"$$\begin{array}{cc}coloumn1& coloumn2\\ \left(a\right)AngleofProjection& \left(p\right)20\\ \left(b\right)Angleofvelocitywithhorizontalafter4s& \left(q\right)80\\ \left(c\right)MaximumHieght& \left(r\right){45}^{\circ }\\ \left(d\right)HorizontalRange& \left(s\right){tan}^{-1}\frac{1}{2}\end{array}$$ "

A virtual image larger than the object can be obtained by?