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 meterial of the bar.

Test dimensionally if the formula t= 2 pi sqrt(m/(F/x)) may be corect where t is time period, F is force and x is distance.

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.

The time period of a simple pendulum is given by the formula, T = 2pi sqrt(l//g) , where T = time period, l = length of pendulum and g = acceleration due to gravity. If the length of the pendulum is decreased to 1/4 of its initial value, then what happens to its frequency of oscillations ?

Show that the time period of a simplw pendulam of infinite length is given by t=2pi sqrt((R)/(g)) where R is the radius of the earth

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.

Find time period of the function, y=sin omega t + sin 2omega t + sin 3omega t