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 .

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.

Check by the method of dimensions, whether the folllowing relation are dimensionally correct or not. (i) upsilon = sqrt(P//rho) , where upsilon is velocity. P is prerssure and rho is density. (ii) v= 2pisqrt((I)/(g)), where I is length, g is acceleration due to gravity and v is frequency.

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.

Check the accuracy of the equation n = (1)/(2l)sqrt((F)/(m)) where l is the length of the string, m its mass per unit length, F the stretching force and n the frequency of vibration.

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 dimensional consistency of the relation upsilon = (1)/(I) sqrt((P)/(rho)) where I is length, upsilon is velocity, P is pressure and rho is density,

Which of the following is not the law of a stretched string ? ( n , l , T and m are frequency of vibration , length of vibrating string , tension in string and linear mass density , respectively .)

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

The mass suspended from the stretched string of a sonometer is 4 kg and the linear mass density of string 4 xx 10^(-3) kg m^(-1) . If the length of the vibrating string is 100 cm , arrange the following steps in a sequential order to find the frequency of the tuning fork used for the experiment . (A) The fundamental frequency of the vibratinng string is , n = (1)/(2l) sqrt((T)/(m)) . (B) Get the value of length of the string (l) , and linear mass density (m) of the string from the data in the problem . (C) Calculate the tension in the string using , T = mg . (D) Substitute the appropriate values in n = (1)/(2l) sqrt((T)/(m)) and find the value of 'n' .