A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s–2. The density of water is 1 gm cm–3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s2).

A metallic sphere cools from 50oC to 40o in 300 s. If atmospheric temperature around is 20oC, then the sphere’s temperature after the next 5 minutes will be close to :

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm–1, density = 667 kg m–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60o with one another. Then h is close to (g = 10 ms–2)

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

Consider a solid sphere of radius R and mass density \rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right) , $$0<r\le R$$ The minimum density of a liquid in which it will float is :

A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :

Two liquids of densities $${\rho }_1$$ an $${\rho }_2$$ ($${\rho }_2$$ = 2$${\rho }_1$$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho$$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $$\omega$$ rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :

Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm–2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube. (density of water = 1000 kgm–3)

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell$$. The other end is fixed. The system is given an angular speed $$\omega$$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx2 and rotating with angular speed $$\omega$$ (see figure). The value of $$\omega$$ is (neglect friction) :

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms–2) is of the order of :

Take the breakdown voltage of the zener diode used in the given circuit as 6V. For the input voltage shown in figure below, the time variation of the output voltage is: (Graphs drawn are schematic and not to scale)

When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is

If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then its band gap energy is : Planck’s constant h = 6.63 $$\times$$ 10–34 J.s. Speed of light c = 3 $$\times$$ 108 m/s

Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

Identify the operation performed by the circuit given below :