A balloon has mass of $$10\mathrm{g}$$ in air. The air escapes from the balloon at a uniform rate with velocity $$4.5\mathrm{cm}/\mathrm{s}$$. If the balloon shrinks in $$5\mathrm{s}$$ completely. Then, the average force acting on that balloon will be (in dyne).

The force required to stretch a wire of cross-section $$1{\mathrm{cm}}^2$$ to double its length will be : (Given Yong's modulus of the wire $$=2\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$$)

A pressure-pump has a horizontal tube of cross sectional area $$10{\mathrm{cm}}^2$$ for the outflow of water at a speed of $$20\mathrm{m}/\mathrm{s}$$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is : [given: density of water $$=1000\mathrm{kg}/{\mathrm{m}}^3$$]

Consider a cylindrical tank of radius $$1\mathrm{m}$$ is filled with water. The top surface of water is at $$15\mathrm{m}$$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $$5\mathrm{m}$$ from the bottom. A force of $$5\times 10^5\mathrm{N}$$ is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure $${\mathrm{P}}_{\mathrm{A}}=1.01\times 10^5\mathrm{Pa}$$, density of water $${\rho }_{\mathrm{W}}=1000\mathrm{kg}/{\mathrm{m}}^3$$ and gravitational acceleration $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$$ )

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R): Because the angle of contact between the oil/grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below.

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $$\sqrt{x(u^2-gL)}$$. The value of x is -

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $$\alpha$$ with respect to point P. Which of the following graphs represent the correct relation between A and $$\alpha$$ when ball goes from Q to R?

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $$\omega$$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $$\mu$$. The beaker will revolve with the disc if :

For a particle in uniform circular motion, the acceleration $$\overrightarrow{a}$$ at any point P(R, $$\theta$$) on the circular path of radius R is (when $$\theta$$ is measured from the positive x-axis and v is uniform speed) :

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is {K \over \pi } rev./min. The value of K is : (Assume the string is massless and unstretchable)

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is $$60\mathrm{m}$$, then the magnitude of displacement would be : (Given $$\cos 135^{\circ }=-0.7)$$

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v) ?

In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p-n junction diode (D1 or D2) is 0.6 V. Which of the following output voltage (V0) waveform across the diode is correct?

In the following circuit, the correct relation between output (Y) and inputs A and B will be :

For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode :

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : n-p-n transistor permits more current than a p-n-p transistor. Reason R : Electrons have greater mobility as a charge carrier. Choose the correct answer from the options given below :