The coefficient of linear expansion of a solid is `alpha` .The temperature at which the density of the solid becomes 5% less than its density at `0^(@)C` is (A) `(1)/(22 alpha)^(@)C` (B) `(1)/(36 alpha)^(@)C` (C) `(1)/(47 alpha)^(@)C` (D) `(1)/(57 alpha)^(@)C`

If coefficient of real expansion of a liquid is (1)/(5500)/^(0)C . The temperature at which its density is 1% less than density at 0^(0)C is

A cube of edge (L) and coefficient of linear expansion (alpha) is heated by 1^(0)C . Its surface area increases by

If two rods of lengths L and 2L having coefficients a and 2a are joined in series Find a of combination. (A) (2)/(3)alpha (B) (1)/(2)alpha (C)(5)/(3)alpha (D) (3)/(6)alpha

The coefficient of linear expansion 'alpha ' of a rod of length 2 m varies with the distance x from the end of the rod as alpha = alpha_(0) + alpha_(1) "x" where alpha_(0) = 1.76 xx 10^(-5) "^(@)C^(-1)"and" alpha_(1) = 1.2 xx 10^(-6)m^(-1) "^(@)C^(-1) . The increase in the length of the rod. When heated through 100^(@)C is :-

For an isotropic solid,if alpha_(x) , alpha_(y) , alpha_(z) represent the mean coefficient of linear expansion along three mutually perpendicular directions then coefficient of volumetric expansion can be written as, A) sqrt(alpha_(x)alpha_(y)alpha_(z)) B) alpha_(x)+alpha_(y)+alpha_(z) C) alpha_(x)alpha_(y)+alpha_(y)alpha_(z)+alpha_(z)alpha_(x) D) alpha_(x)alpha_(y)alpha_(z)

" The relation between coefficient of linear expansion "(alpha_(1))" and coefficient of volume expansion ( "alpha_(5)" ) is "

The diameter of a metal ring is D and the coefficient of linear expansion is alpha . If the temperature of the ring is increased by 1^(0)C , the circumference and the area of the ring will increases by

If pi

Givent that (pi)/(2)

Let A(alpha)=[cosalpha0sinalpha0 1 0sinalpha0cosalpha] and X is a set of all matrices A(alpha) for different values of alpha . Which of the following is true (a)A^(-1)(alpha)=A(-alpha) (b) A^(-1)(alpha)=A(alpha) (c)det(a d j(A^(-1)(alpha)))=sec^2 2alpha (d)det(A^(-1)(alpha))=1/(cos2alpha)