The percentage errors in the measurement of mass and speed

The percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in kinetic energy obtained by measuring mass and speed will be

Percentage error in mass			∆m	× 100		= 2 and percentage error in speed			∆v	× 100
			m						v

⇒	∆v	=	3	and	∆m	=	2
	v		100		m		100

Kinetic energy =	1	mv² ∝ mv²
	2

∴ Error in measurement of kinetic energy =		∆m	+ 2			∆v
		m				v

By Binomial Function ,

Req. error =		∆m		+		2 ×	∆v
		m					v

=		2		+		2 ×	3		=	8	= 8%
		100					100			100

∴ %age error = 8%.