Question

A small block starts slipping on a smooth inclined plane from rest. If the distance travelled in time interval from t = (n - 1) to t = n, be Sn, then the value \(\frac{Sn}{s_{n + 1}}\) will be:

(a) \(\frac{(2n - 1)}{2n}\)

(b) \(\frac{2n + 1}{2n - 1}\)

(c) \(\frac{2n - 1}{2n + 1}\)

(d) \(\frac{2n}{2n + 1}\)

Answer 1

Distance travelled in nth second

St = ut + \(\frac{1}{2}a(2t - 1)\)

or St = u + at \(-\frac{1}{2}a\)

It is given that u = 0

∴ St = \(at - \frac{1}{2}a\) 

\(\therefore\ \frac{S_n}{S_{n + 1}} = \frac{an -\frac{1}{2}a}{a(n + 1) - \frac{1}{2}a } = \frac{2n - 1}{2n + 1}\) 

Therefore, option (c) is correct.