A rod of length 2m at` 0^(@)C` and having expansion coefficient `a=(3x+2)times10^(-6)` `c^(-1)` where x is the distance (in cm ) from one end of rod.The length of rod at `20^(@)C` is :

The density of a rod of length L varies as rho=A+Bx where x is the distance from the left end. Locate the centre of mass.

The coefficient of linear expansion of a rod of length 1 m, at 27^@C , is varying with temperature as alpha = 2/T unit (300 K le T le 600 K) , where T is the temperature of rod in Kelvin. The increment in the length of rod if its temperature increases from 27^@C to 327^@C is

A rod is of length 3 m and its mass acting per unit length is directly proportional to distance x from its one end. The centre of gravity of the rod from that end will be at

The linear density of a thin rod of length 1m lies as lambda = (1+2x) , where x is the distance from its one end. Find the distance of its center of mass from this end.

A rod hanging from ceiling has linear density given as lambda=m_0(1+x) kg/m, where m_0 is constant and x is distance of a point from free end . if the length of the rod is 4m then velocity of wave at x=1m is

A thin rod of negligible mass and a cross-section of 2 xx 10^(-6) m^(2) suspended vertically from one end, has a length of 0.5 m at 200^(@)C . The rod is cooled at 0^(@)C , but prevented from contracting by attaching a mass at the lower end. The value of this mass is : (Young's modulus =10^(11) N//m^(2) , Coefficient of linear expansion 10^(-5) K^(-1) and g = 10 m//s^(2) ):

An thin rod of negligible mass and area of cross - section 4xx10^(-6)m^(2) , suspended vertically from one end, has a length of 0.5 m at 100^(@)C . The rod is cooled to 0^(@)C but prevented from contracting by attaching a mass at the lower end. The value of this mass is (Given, coefficient of linear expansion is 10^(-5^(@))C^(-1) , Young's modulus is Y=10^(11)Nm^(-2) and g=10ms^(-2))

A rod length L and mass M is placed along the x -axis with one end at the origin, as shown in the figure above. The rod has linear mass density lamda=(2M)/(L^(2))x, where x is the distance from the origin. Which of the following gives the x -coordinate of the rod's center of mass?

A steel rod of length 25cm has a cross-sectional area of 0.8cm^(2) . The force required to stretch this rod by the same amount as the expansion produced by heating it through 10^(@)C is (alpha_(steel)=10^(-5)//^(@)C and Y_(steel)=2xx10^(10)N//m^(2))

Three rods of copper, brass and steel are welded together to form a Y -shaped structure. The cross-sectional area of each rod is 4 cm^2 . The end of copper rod is maintained at 100^@C and the ends of the brass and steel rods at 80^@C and 60^@C respectively. Assume that there is no loss of heat from the surfaces of the rods. The lengths of rods are : copper 46 cm, brass 13 cm and steel 12 cm. (a) What is the temperature of the junction point? (b) What is the heat current in the copper rod? K(copper) = 0.92, K (steel) = 0.12 and K(brass) = 0.26 cal//cm-s^@C .