Find the dimensions of the quantity q from the expression `T = 2pi sqrt((ml^3)/(3Yq)),` where T is time period of a bar of length l, mass m and Young's modulus Y.

Find the dimensions of the quantity q from the expression : T = 2pi sqrt((ml^3q)/(5Y)), Where T is tiem period of a bar of length I, mass m and Young's modulus Y.

Find the dimensions of K in the relation T = 2pi sqrt((KI^2g)/(mG)) where T is time period, I is length, m is mass, g is acceleration due to gravity and G is gravitational constant.

By the method of dimensions, test the accuracy of the equation : delta = (mgl^3)/(4bd^3Y) where delta is depression in the middle of a bar of length I, breadth b, depth d, when it is loaded in the middle with mass m. Y is Young's modulus of material of the bar.

By the method of dimensions, test the accuracy of the equation : delta = (mgl^3)/(4bd^3Y) where delta is depression in the middle of a bar of length I, breadth b, depth d, when it is loaded in the middle with mass m. Y is Young's modulus of meterial of the bar.

Check the dimensional correctness of the following equations : (i) T=Ksqrt((pr^3)/(S)) where p is the density, r is the radius and S is the surface tension and K is a dimensionless constant and T is the time period of oscillation. (ii) n=(1)/(2l)sqrt((T)/(m)) , when n is the frequency of vibration, l is the length of the string, T is the tension in the string and m is the mass per unit length. (iii) d=(mgl^3)/(4bd^(3)Y) , where d is the depression produced in the bar, m is the mass of the bar, g is the accelaration due to gravity, l is the length of the bar, b is its breadth and d is its depth and Y is the Young's modulus of the material of the bar.

Find the value of x in the relation Y = (T^x . Cos theta. Tau)/(L^3), where Y is Young's modulu. T is time period, tau is torque and L is length.

If the depression d at the end of a loaded bar is given by d = (Mg l^3)/(3 yi) where M is the mass , l is the length and y is the young's modulus, then i has the dimensional formula