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19)With usual notation, the following equation, said to give thedistance covered in the nth second. i.e.,(2n - 1)2is(a) numerically correct only(b) dimensionally correct only(c) both dimensionally and numerically only(d) neither numerically nor dimensionally correct

Answer»

Here,S=u+(1/2)*a*(2n-1) this equation is used to find distance travelled by body in nth second.

LHS

So,S(nth) = distance travelled in nth second

i.e S(nth) = [L]/[T] = [LT^-1] dimensionally

RHS

Now,U+(1/2)*a*(2n-1) = where,

U= initial velocity = [LT^-1]

a= acceleration = [LT^-2]

2n-1= n=time = [T]

1/2=dimensionless = [M°L°T°]

——————————————————

U+(1/2)*a*(2n-1)= [LT^-1]+[LT^-2]*[T]

[LT^-1]+[LT-^1]=[LT^-1] by principle of homogeneity.

As LHS= RHS dimensionally i.e [LT^-1]

Therefore, it is dimensionally correct.

option (c) is correct.

but how can say that this equation will be numerically correct


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