Question

14. Mass of a body is (10 +-0.1) kg. Volume is (1 +- 0.1).
m. Then density (p) is given as
(1) (10 +-1.1) kg m-3 (2) (10 +- 0.11) kg m-3
(3) (10 +-0.01) kg m-3 (4) (10 +-0.21) kg m-3
V
m2​

Answer 1

answer : option (1) (10 ± 1.1) kg/m³

explanation : mass of body, M = (10 ± 0.1) kg

volume of body, V = (1 ± 0.1) m³

we know, density is the ratio of mass and volume. i.e., d = M/V

first of all, find value of d without including error.

if mean, take M = 10, V = 1

and then density , d = 10/1 = 10 kg/m³

now find error in density by using formula

∆d/d = ∆M/M + ∆V/V

where , d = 10, ∆M = 0.1 , M = 10, ∆V = 0.1 and V = 1

then ∆d/10 = 0.1/10 + 0.1/1

or, ∆d = 10(0.01 + 0.1) = 10(0.11) = 1.1

hence, appreciate value of density is (10 ± 1.1) kg/m³.

therefore option (1) is correct choice.

Answer 2

Answer:

10 ± 1.1 kg/m³

Explanation:

Density = Mass / Volume

Mass = 10 ± 0.1 kg

Volume = 1 ± 0.1 m³

Density = 10/1  ± 0.1/10 ± 0.1/1

10 ± 0.01 ± 0.1

= 10 ± 1.1 kg/m³