A rod of length 2m at 0 0 C and having expansion coefficient α=(3x+2)×10 −6 / 0 C where x is the distance (in cm) from one end of rod. The length of rod at 20 0 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 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 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

The liner density of a rod of length 2m varies as lambda = (2 + 3x) kg/m, where x is distance from end A . The distance of a center of mass from the end B will be

Two rods of equal cross sections, one of copper and the other of steel, are joined to form a composite rod of length 2.0 m at 20^@C , the length of the copper rod is 0.5 m. When the temperature is raised to 120^@C , the length of composite rod increases to 2.002m. If the composite rod is fixed between two rigid walls and thus not allowed to expand, it is found that the lengths of the component rods also do not change with increase in temperature. Calculate Young's moulus of steel. (The coefficient of linear expansion of copper, alpha_c=1.6xx10^(-5@)C and Young's modulus of copper is 1.3xx10^(13)N//m^(2) ).

The density of a thin rod of length l varies with the distance x from one end as rho=rho_0(x^2)/(l^2) . Find the position of centre of mass of rod.

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?

An iron rod of length 50 cm is joined at an end to aluminium rod of length 100 cm. All measurements refer to 20^(0) C . Find the length of the composite system at 100^(o) C and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminium are 12 X 10^(-6 ) C^(-1) and 24 X10^(-6 ) C ^(-1) respectively.

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 .

An iron bar of length 10 m is heated from 0^@C " to " 100^@C . If the coefficient of linear thermal expansion of iron is 10xx10^(-6) .^@C^(-1) , then increase in the length of bar (in cm ) is