A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water fw = 1000 kg m$$-$$3 and Density of air fa = 1.2 kg m$$-$$3, g = 10 m/s2, Coefficient of viscosity of air = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2]

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $$\times$$ 10$$-$$2 Nm$$-$$1, angle of contact = 0, g = 10 ms2 and density of water = 1.0 $$\times$$ 103 kg m$$-$$3]

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is {{24} \over \pi } \times {10^2} Nm-2. What is the minimum radius of the wire ? (Take g = 10 ms-2)

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10$$-$$5 m and density 1.2 $$\times$$ 103 kgm$$-$$3 ? Take viscosity of liquid = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2. (Neglect buoyancy due to air).

A uniform heavy rod of weight 10 kg ms$$-$$2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 1011 Nm$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 1011 Pa, g = 9.8 m/s2]

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3. Its time period of revolution will be given by :

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is :

Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh$$-$$1 and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s2) Statement II : If the road is banked at an angle of 45$${}^{\circ }$$, cyclist can cross the curve of 2m radius with the speed of 18.5 kmh$$-$$1 without slipping. In the light of the above statements, choose the correct answer from the options given below.

A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is $$\mu$$s, then the magnitude of negative lift FL acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)

A particle of mass m moves in a circular orbit under the central potential field, U(r) = - {C \over r}, where C is a positive constant. The correct radius $$-$$ velocity graph of the particle's motion is :

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$${}^{\circ }$$ banked road at maximum possible speed without skidding is ____________ $$\times$$ 103 kg m/s2. [Given cos30$${}^{\circ }$$ = 0.87, $$\mu$$s = 0.2]

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r = {L \over {\sqrt 2 }}. The speed of particle will be :

A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second? Given : 1 ly = 9.46 $$\times$$ 1015 m 1 AU = 1.5 $$\times$$ 1011 m

If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of $$\beta$$ will be :

The logic circuit shown above is equivalent to :

Given below are two statements : Statement I : PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement II : In the study of transistor, the amplification factor $$\beta$$ indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below.

Zener breakdown occurs in a p $$-$$ n junction having p and n both :

A 5V battery is connected across the points X and Y. Assume D1 and D2 to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.

For extrinsic semiconductors; when doping level is increased;