[" 1.Derive "f=(1)/(2/)sqrt((T)/(m))" dimensionally,where "f" is frequency,"" lis the length,"T" is the tension and "m" is the "],[" mass per unit length."]

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.

Check the accuracy of the relation v=(1)/(2l)sqrt((T)/(m)) ,where v is the frequency, l is legth, T is tension and m is mass per unit legth of the string.

Check the accuracy of the relation v=(1)/(2l)sqert((T)/(m)) ,where v is the frequency, l is legth, T is tension and m is mass per unit legth of the string.

Chack the correctness of the relations. (i) escape velocity, upsilon = sqrt((2GM)/(R )) (ii) v =(1)/(2l) sqrt((T)/(m)) , where l is length, T is tension and m is mass per unit length of the string.

Establish by dimensional analysis that v= sqrt(T/m) where v is the velocuty of wave along the stretched wire.T is tension applied and m is mass per unit length of the wire.

The frequency (n) of vibration of a string is given as n = (1)/( 2 l) sqrt((T)/(m)) , where T is tension and l is the length of vibrating string , then the dimensional formula for m is

The frequency (n) of vibration of a string is given as n = (1)/( 2 l) sqrt((T)/(m)) , where T is tension and l is the length of vibrating string , then the dimensional formula is

Check by the method of dimensions whether the following relations are true. (i) t=2pisqrt(l/g) , (ii) v=sqrt(P/D) where v= velocity of sound P=pressure D=density of medium . (iii) n=1/(2l)=sqrt(F/m) where n= frequency of vibration l=length of the string, F=stretching force m=mass per unit length of the string .

Explain with example, how dimensional analysis is used to derive the relation, n=frac(1)(2L)sqrtfrac(T)(m) where n rarr Frequency, T rarr Tension, L rarr Length, m rarr mass per unit length.

Derive the folowing relation by the method of dimensions v=sqrt(T/mu) T=Tension, mu =mass per unit length.