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Force F is given in terms of time t and distance ‘x’ by F = A sin Ct + B cos Dx. Then dimensions of A/B and C/D are
(a) [M0L0T0], [M0L0T–1]
(b) [MLT–2], [M0L–1T0]
(c) [M0L0T0], [M0LT-1]
(d) [M0L–1T-1], [M0L0T0]
(a) A/B=Force/Force [M^o L^o T^o ] ct = angle C = angle/time=1/T=T^(-1) Dx = angle D = angle/distance=1/L = L–1 C/D=T^(-1)/L^(-1) =[M^o LT^(-1) ]
A/B= no dimensions, C/D= LT^(-1)
Explanation:
obviously...Ct & Dx indicate the angles
Ct = radians
Dx = radians
C = radians/sec
D = radians/metre
since sinCt & sinDx are simply numericals hence A & B indicate Force components
A = Newtons
B = Newtons
Now,
C/D = [radions/sec]/radions/metre]= metre/sec =LT^(-1)
A/B = Newtons/Newtons is a ratio and no dimensions
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