A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that any be given to a similar rope of diameter 2 cm is

Options

A. 2000 N
B. 1000 N
C. 500 N
D. 250 N

Answer

a

Explanation

We know that
young modulus `Y =("stress") /("strain")`
`y=(T)/(Axx"Strain")`
for same type of wire
`(y)/("strain")=(T)/(A) rarr (T_(1))/(A_(1))=(T_(2))/(A_(2))`
where T s are tensions in the wires and A 's are areas of cross section
or `(500)/(pir_(1)^(2))=(T_(2))/(pir_(2)^(2))` or `(500)/((1cm)^(2))=(T_(2))/(2cm)^(2)`
`T_(2)=4xx500=2000 N`