KVPY SA Exam 2015 Question Paper

Question : 16 of 80

Marks: +1, -0

PHYSICS

In an experiment, mass of an object is measured by applying a known force on it, and then measuring its acceleration. If, in the experiment, the measured values of applied force and the measured acceleration are F = 10.0 ± 0.2 N and a = 1.00 ±0.01 m/

s^2

, respectively, the mass of the object is

10.0 Kg
10.0 ± 0.1 Kg
10.0 ± 0.3 Kg
10.0 ± 0.4 Kg

Validate

Solution:

Force F = 10.0 ± 0.2 N
a = 1.00 ± 0.01 m/s

^2

F = ma ⇒ m =F/a

m=10.0/1.00

m = 10.0 kg
For error (F = ma)

m ^{1 }a ^{1} F^{-1} =

const.

{dm}/m+{da}/a-{dF}/F=0

[Take log and differentiate]

{ ∆ m}/m={|{ ∆ F}/F-{ ∆ a}/a|}_\max

{ ∆ m}/m={| 0.2/10.0+0.01/1.00|}

{ ∆ m}=3/100m

{ ∆ m}=3/100×10

∆ m=0.3

kg
mass m = (10.0 ± 0.3 kg)

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