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Which of the following graphs represent the relation between capillary rise h and more radius of capillary tube r?

The condition for a uniform spherical mass m of radius r to be a black hole is ..... (G = gravitational constant and g = acceleration due to gravity)

Match the following

A: A spinning cricket ball moving through air is not deflected from its normal trajectory R: Magnus effect is an application of Bernoulli.s principle

A body is projected vertically upward with the velocity v=3hati+4hatjms^(-1). The maximum height attained by the body is (g=10ms^(-2)).

Increase of pressure

Which of the diagrams correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient depth to impart it a terminal velocity ?

Find the time period of mass M when displaced from its equilibrium position and then released for the system shown in figure. .

Let f be the fundamental frequency of the string . If the string is divided into three segments l_(1) , l_(2) and l_(3) such that the fundamental frequencies of each segments be f_(1) , f_(2) and f_(3) , respectively . Show that(1)/(f) = (1)/(f_(1)) + (1)/(f_(2)) + (1)/(f_(3))

A car is negotiating a curved road of radius R. The road is banked at an angle. The coefficient of friction between the types of the car and the road is mu_(s). The maximum safe velocity on this road is

In case of an orbiting satellite, if the radius of orbit is decreased, then (a) its KE decreases (b) its PE decreases (c) its mechanical energy decreases

A wire of length 1 m and radius 1 mm is subjected to a load. The extension is x. The wire is melted and then drawn into a wire of square crosssection of side Imm. What is the extension under the same load ?

In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation what will be the maximum deformation in the spring? Consider all the strings to be sufficiency large. Consider the spring constant to be K.

The initial phase of body executing SHM is (pi)/(4), then what will be its phase at the end of 10 oscillations?

A boat moves perpendicular to the bank with a velocity of 7.2km ph . The current carries it 150m downstream. Find the velocity of current and the time required to cross the river. Width of the river is 0.5km.

The apparent weight of man inside a lift moving up with certain acceleration is 900N. When the lift is coming down with the same acceleration apparent weight is found to be 300 N. The mass of the man is (g=10 ms^(-2))

A specific gravity bottle weighs 20.5 gm when it is empty. When it is filled with a liquid at 20^(@)C it weighs 45.2 gm. The bottle with the liquid at 100^(@)C weighs 43.2 gm. Calculate the coefficient of apparent expansion of the liquid.

Four spheres A, B, C, D, each of mass m and diameter 2 a are placed with their centres at die four corners of a square of side b. What is the moment of inertia of the system about any side of the square ?

For a gas molecule with 6 degrees of freedom the law of equipartition of energy gives the following relation between the molar specific heat (C_(V)) and gas constant (R )

Which of the following is incorrect regarding the first law of thermodynamics?

A body is throw up with a velocity 'u'. It reaches maximum height 'h'. If its velocity of projection is doubled the maximum height it reaches is _____

A body is performing simple harmonic motion. Then its:

A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the tow parts taken together shifts horizontally towards

A wire has a mass (0.2 +- 0.002) g, radius (0.7+-0.007) mm and length (3 +- 0.09) cm. The maximum percentage error in the measurement of its density is

A wheel of M.I. 0.1" kg m"^(2) is rotating at a speed of 1200 rpm. Now it is slowed down uniformly such that it comes to rest after making 314 complete revolution. The magnitude of the retarding torque is

Mark the incorrect statement

Which one of the following Cartesian coordinate systems is not follwed in physics?

If the inter - molicule potential energy is minimum at separation R0 what prevents the molecules ofa a substance from collasping to the condensed state ?

Portion AB of the wedge shown in fig is rough and BC is smooth. A solid cylinder rolls without slipping from A to B. AB = BC, then ratio translational kinetic energy to rotational kinetic energy, when the cylinder reaches point C is

A uniform circular disc of mass m is set rolling on a smooth horizontal table with a uniform linear velocity v. Find the total K.E. of the disc.

If the terminal speed of a sphere of gold (density =19.5kgm^(-3)) density of liquid =1.5kgm^(-3)) is 0.2ms^(-1) in a viscous liquid . What is the terminal speed of a sphere of silver (density =10.5kgm^(-3)) of the same size in the same liquid ?

If the gravitational force between two objects were propotional to 1/R (and not as 1//R^(2)) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

Consider a Carnot.s cycle operating between T_(1)=500K and T_(2)=300K producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

Particles of masses 10 g and 20 g have position vectors (5,3,0) and (2,0,3) respectively. The position vector of their centre of mass is ………… cm.

In the arrangement shown in figure pulley is smooh and massless and string is light .Frication coeffcient between A and B is mu friction is absentbetweenA and plane .Selcet the correct alternative(s) .

Equation of a plane progressive wave is given by y = 0.6 sin 2pi (t - (x)/(2)).On reflection from a denser medium its amplitude becomes (2)/(3)of the amplitude of the incident wave. The equation of the reflected wave is ..........

Determine the pressure requirred to reduce the given volume of water by 2%. Bulk modulus of water is 2.2xx10^(9)Nm^(-2)

Consider the following statements and choose the correct answer. a) if heat is added to a system, its temperature must always increase. b) if positive work is done by a system in thermodynamics process, its volume must increase.

Maximum speed of a particle in simple harmonic motion is v_(max). Then average speed of this particle in one time period is equal to

Show that (P^(-5//6)rho^(1//2)E^(1//3)) is of the dimension of time. Here P is the pressure, rho is the density and E is the energy of a bubble).

A stone is dropped from a hill of height 180m. Two seconds later another stone is dropped from a point P below the top of the hill . If the two stones reach the ground simultaneously , the height of P from the ground is (g=10ms^(-2))

Is the bulb of a thermometer made of diathermic or adiabatic wall ?

Displacement time equation of a particle executing SHM is x = a sin (wt+pi//16). Time taken by the particle to go directly from x = -A//2 to x = + A//2 is