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State the principle of homogeneity. Test...

State the principle of homogeneity. Test the dimensional homogeneity of equations—
`S_(n)=u+(a)/(2)(2n-1)`

Text Solution

Verified by Experts

`S_(n)` = Distance travelled in `n^(th)` sec that is `(S_(n)-S_(n-1))`
`therefore S_(n)=uxx1+(a)/(2)(2n-1)`
`[LT^(-1)]=[LT^(-1)]+[LT^(-2)][T]`
`[LT^(-1)]=[LT^(-1)]`
L.H.S. = R.H.S.
Hence this is dimensionally correct.
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Knowledge Check

  • The distance travelled by a body moving along a straight line with uniform acceleration (a) in the nth second of its motion is given by S_(n)=u+(a)/(2)(2n-1) . This equation is

    A
    only numerically correct only
    B
    only dimensionally correct only
    C
    correct both dimensionally and numerically
    D
    neither numerically nor dimensionally correct

  • Statement-1: A formula derived using dimensional analysis obeys principle of homogenity . Statement:-2: A physically correct relation is always in accordance with principle of homogenity

    A
    Statement-1 is true and statement -2 is true
    B
    Statement -1 is true and statement-2 is false
    C
    Statement-1 is false and statement -2 is true
    D
    Statement-1 is false and statement -2 is false

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