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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)
(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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