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An aeroplane takes flight from a place towards another place in directiontheta N of E in a strong wind of velocity U to the west. The speed of plane in still air is V. Distance the two places is L At what angle the plane must be driven wrt line of flight

An aeroplane takes flight from a place towards another place in direction thetaN of E in a strong wind of velocity U to the west. The speed of plane in still air is V. Distance the two places is L If T_(1), T_(2)are time of travel of on ward and return journey, thenT_(1) T_(2)= ..........

Rain is falling vertically with a speed of 35ms^(-1). Winds starts blowing after sometime with a speed of 12ms^(-1) in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella?

A soundof frequency 1000 Hz is emitted from a roadside siren. A car moving along the road with a unifrom velocity of 50 km . h^(-1) crosses the siren . Calculate the frequency of the siren relative to the pasenger of the car before and after crossing the siren . (Velocity of sound = 340 ms^(-1))

Can we add velocity-vector to the displacement vector?

An open organ pipe of length l vibrates with its fundamental note. The presure variation is maximum.

Statement A: At absolute zero the substancehas internal energy due to the vibrational motion of atoms with in the molecules. This is zero point energy. Statement B: First law of thermodynamics does not satisfy the condition under which a body can use its heat energy to produce the work.

A packet is dropped from a balloon rising up with uniform velocity 9.8ms^(-1). If the balloon is at a height of 39.2 m from the ground at the time of dropping the stone, the stone reaches the ground after

The temperatures of two bodies measured by a thermometer are t_(1) = (20 pm 0.5)^(@)C, t_(2) = (50 pm 0.5)^(@)C. Calculate the temperature difference and the error therein.

Pressure exerted by a gas is .............. .

A force F varies with time in accordance with the following figure. The mean force for one cycle.

The direction cosines of a vector vecA are cos alpha=(4)/(5sqrt(2)), cos beta = (1)/(sqrt(2)) and cos gamma = (3)/(5sqrt(2)), then the vector vecA is

''A hot liquid' remains hot and a cold liquid remains cold in a thermos flask.'' Explain how ?

If the angular speed of earth increases two times then the acceleration of gravity (g) at north pole becomes .......

A ballis thrown upward with an initial velocity of 100ms^(-1). After how much time will it return? Draw velocity - time graph for the ball and find from the graph (i) the maximum height attained by the ball and (ii) height of the ball after 15 s. Take g=10ms^(-2).

If the unit of force is 2N, that of length is 4m and that of velocity is 6ms^(-1), the unit of mass is

Give difference between path length and displacement.

When 0.15 kg of ice at 0 ^(@) 0is mixed with 0.30 kg of water at50 ^(@) Cin a container, the resulting temperature is6.7 ^(@) C . Calculate the heat of fusion of ice. (S_("water") = 4186 J kg^(-1) K^(-1))

What is the gravitational potential at infinity distance from the centre of earth ?

Calculate the temperature at which the oxygen molecules will have the same rms velocity as the hydrogen molecules at 150^@C. Molecular weight of oxygen is 32 and that of hydrogen is 2.

A body projected obliquely with velocity 19.6 ms^(-1)has its kinetic energy at the maximum height equal to 3 times its potential energy there. Its position after 1 second of projection from the ground is (h= maximum height)

A body starts from rest from a point distance RQ from the surface of the earth. The velocity acquired by the body when it reaches the surface of the earth will be (R —> Radius of the earth) (R_(0) gt R)

A stone is thrown vertically upwards from some high point P. The velocity of the stone at a height h above P is half that at a depth h below P. The maximum height attained by the stone is

A particle moves in the plane XY with constant acceleration a directed along he negtive Y-axis. The equation of motion of the particle has the form y=Ax-Bx^(2), where A and B are positive constants. Find the velocity of the particle at the origin of the coordinates.

A particle is going parallel to x-axis with constant speed V at a distance 'a' from the axis. Find its angular velocity about an axis passing the origin O, at the instant when radial vector of the particle makes angle theta with the x-axis

A shell is fired from the ground at an angle with horizontal with a velocity 'v'. At its highest point it breaks into two equal fragments. If one fragment comes back through its initial line of motion with same speed, then the speed of the second fragment will be

A Geo-stationary satellite bits around the earth in a circular of radius 36, 000 km then what will be the time period of a spy satellite orbiting a few hundred km above the earth's surface (R_("earth") = 6400 km)

In the above problem its velocity after 3 seconds inms^(-1) is

A person can swim in still water at 5 m/s. He moves in a river of velocity 3 m/s. First down the stream next same distance up the steam the ratio of times taken are

A train of 150 metre length is going towards north direction at a speed of 10 m/s. A parrot flies at the speed of 5 m/s towards south direction parallel to the railways track. The time taken by the parrot to cross the train is

A beam of light of red and green rays is incident obliquely at a point on a face of rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from

Calculate work done to move a boy of mass 20 kg along an inclined plane (theta = 45^(@)) with constent velocity through a distance of 10 m.

The circular scale of a screw gauge has 50 divisions and pitch of 0.5 mm. Find the diameter of sphere. Main scale reading is 2.

Spinning of the Earth about its own axis is known as .............. motion.

A spring of force constant k is stretched by a small length x. The work done in stretchign it further by a small length y is

A cyclist travels with a speed of 36 km^(-1)if the angleof inclinatio withvertical is 45^(@)whilehe goes around a circle then the radius of the circle is

For the travelling harmonic wave y(x,t) =2.0 cos 2pi [8t-0.0060x + 0.27], where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of, (a) 300 cm, (b) 0.75 m, ( c) lambda/4

A sphere of mass 50 gm and diameter 2 cm rolls without slipping with a velocfty of 5 cm/s. Calculate the total energy.

What is the radius of gyration?

Suppose speed of light (c), force (F) and kinetic energy (K) are taken as the fundamental units, then the dimensional formula for mass will be

When a system is induced to oscillation, say whether the system oscillation to its natural frequency force?