The time T taken by a spring-mass system to complete one oscillation is given by

Question

The time T taken by a spring-mass system to complete one oscillation is given by T = 2 pi Squareroot m/k where m = mass and k is called spring constant. What should the dimensions of k be if this equation is true? a) (T)^2/(M) b) (M)^2/(T) c) (M)/(T)^2 d) (M)/(T) (e) None of these Ball A is dropped from rest from a window. At the same instant ball B is thrown downward; and ball C is thrown upward from the same window. Which statement concerning the balls after their release is necessarily true if air resistance is neglected? a) At some instant after it is thrown, the acceleration of ball C is zero (b) All three balls strike the ground at the same time c) All three balls have the same velocity at any instant.

Explanation / Answer

the time period T=2*3.14*[m/K]^1/2

K=4*3.14*[m/t^2]

so the dimension formula for spring constant

the spring constant K=[M T^-2]

the correct option is C

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