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Out of the following expressions for couple per unit twist, time period of a compound pendulum, time period of a simple pendulum and frequency of a stretched wire respectively, the dimensionally consistent expressions are (a) C = (πηr^4)/2l (b) T = 2?√((K^2+l)/g) (c) T = 2?√(l/g) (d) f = 1/l √(T/m)

Out of the following expressions for couple per unit twist, time period of a compound pendulum, time period of a simple pendulum and frequency of a stretched wire respectively, the dimensionally consistent expressions are
    (a)    C = (πηr^4)/2l
    (b)    T = 2?√((K^2+l)/g)
    (c)    T = 2?√(l/g)
    (d)    f = 1/l √(T/m)

Grade:upto college level

1 Answers

Simran Bhatia
348 Points
10 years ago

(a, c, d)

 

(a)    is consistent, C is torque per unit twist, h is modulus of rigidity, r is radius,  is length

 

(c)    is consistent

 

(d)    is consistent, f is frequency, T is tension, m is mass per unit length

 

(b)    is inconsistent, T is time period, k is the radius of gyration, g is acceleration due to gravity.

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