(a) A steel wire of mass u per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform an lateral strains lt lt longitudinal strains find the extension in the length of the wire. The density of steel is 7860 kgm ^(-3) and Young's modulus =2 xx 10 ^(11) Nm ^(-2) (b) If the yield strength of steel is 2.5 xx 10 ^(8) Nm ^(-2), what is the maximum weight that can be hung at the lower end of the wire ?

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the of wire has a length of 1m at 10^@C. Now the end P is maintained at 10^@C, while the ends S is heated and maintained at 400^@C. The system is thermally insultated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2xx10^-5K^-1, the change in length of the wire PQ is

A steel wire of length 5 m and diameter 10^(-3) m is hanged vertically from a ceiling of 5.22 m height. A sphere of radius 0.1 m and mass 8tt kg is tied to the free end of the wire. When this sphere is oscillated like a simple pendulum, it touches the floor of the room in its velocity of the sphere in its lower most position. Calculate the velocity of the sphere in its lower Young's modulus for in its lower most position. Young's modulus for steel =1.994 xx 10 ^(11) Nm ^(-2).

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman's time.In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectivelh, find the maximum profit of the factory when it works at full capacity.

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour or craftman's time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectively, find the maximum profit of the factory when it works at full capacity.

An experimental setup of verification of photoelectric effect is shown in the diagram. The voltage across the electrode is measured with the help of an ideal voltmetar, and which can be varied by moving jockey 'J' on the potentiometer wire. The battery used in potentiometer circuit is of 20 V and its internal resistance is 2omega . The resistance of 100 cm long potentiometer wire is 8 omega . The photo current is measured with the help of an ideal ammeter. Two plates of potassium oxide of area 50 cm^(2) at separation 0.5 mm are used in the vacuum tube. Photo current in the circuit is very small so we can treat potentiometer circuit an indepdent circuit. The wavelength of various colours is as follows : |{:("Light",underset("Violet")(1),underset("Blue")(2),underset("Green")(3),underset("Yellow")(4),underset("Orange")(5),underset("Red")(6)),(lambda "in" Årarr,4000-4500,4500-5000,5000-5500,5500-6000,6000-6500,6500-7000):}| It is found that ammeter current remians unchanged (2muA) even when the jockey is moved from the 'P' to the middle point of the potentiometer wire. Assuming all the incident photons eject electron and the power of the light incident is 4 xx 10^(-6) W . Then colour of the incident light is :

1MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if (a) power is transmitted at 220V. Comment on the feasibility of doing this. (b) a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transformer is used to bring voltage to 220 V. (rho_(cu)=1.7xx10^(-8) SI unit )

A copper wire has diameter 0.5 mm and resistivity of 1.6 xx 10^(-6) Omega m. What will be the length of this wire to make its resistance 10Omega ? How much does the resistance change if the diameter is doubled?

A planet of radius R=(1)/(10)xx(radius of Earth) has the same mass density as Earth. Scientists dig a well of depth (R )/(5) on it and lower a wire of the same length and a linear mass density 10^(-3) kg m(_1) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it inplace is (take the radius of Earth =6xx10^6m and the acceleration due to gravity on Earth is 10ms^(-2)

What is the excess pressure inside a bubble of soap solution of radius 5.00 mm. given that the surface tension of soap solution at the temperature (20^@C) is 2.50 times 10^-2 N m^-1 ? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container the soap solution (of relative density 1.20] what would be the pressure inside the bubble?[1 atmospheric pressure is 1.01 times 10^5 Pa ).