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Q.

The distance travelled by a particle in nthsecond is Sn=u+a2(2n-1) where u is the velocity and a is the acceleration. The equation is

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a

Dimensionally true

b

A and C are correct

c

Dimensionally false

d

Numerically may be true or false

answer is A.

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Detailed Solution

Sn=S1-S2

Sn=un+12an2-u(n-1+12a(n-1)2)  Sn=un+12an2-un-u+12a(n2+1.1-2n(1))Sn=un+12an2-un+u.1-12an2-12a.1.1+12a.2.n(1)Sn=u.1+a2(2n.1-1.1) Here n and 1 are the magnitudes of time and measured in seconds.D.F of L.H.SSn=L

R.H.S D.F of u.1=LT-1.T=LD.F of a2(2n.1-1.1)=LT-2T.T-T.T=LT-2T2=LR.H.S=L+L=L

L.H.S = R.H.S

  Hence the formula is dimensionally correct.

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