Question

A body travels uniformly a distance of $(13.8\pm 0.2)m$ in a time $(4.0\pm 0.3)s$ . The velocity of the body within error limits is:

• A. $(3.45\pm 0.2)m{s}^{-1}$
• B. $(3.45\pm 0.3)m{s}^{-1}$
• C. $(3.45\pm 0.4)m{s}^{-1}$
• D. $(3.45\pm 0.5)m{s}^{-1}$

Answer 1

Answer: (B)

$(3.45\pm 0.3)m{s}^{-1}$

Given,

$s=(13.8\pm 0.2)m$

$t=(4.0\pm 0.3)s$

velocity,

$v=\frac{13.8}{4}=3.45m/s$. . . . . . . .(1)

We know that,

$\frac{\Delta v}{v}=\frac{\Delta s}{s}+\frac{\Delta t}{t}$

$\frac{\Delta v}{v}=\frac{0.2}{13.8}+\frac{0.3}{4}=0.089$

$\Delta v=0.098\times v=0.089\times 3.45=0.3m/s$ (from equation 1)

Velocity of the body within the error limit is,

$v=(v\pm \Delta v)m/s$

$v=(3.45\pm 0.3)m/s$

The correct option is B.