An engine can pull four coaches at a maximum speed of `20ms^-1`. The mass of the engine is twice the mass of every coach. Assuming resistive forces to be proportional to the weight, approximate maximum speeds of the engine, when it pulls `12` and `6` coaches, are

Options

A. 8.5 m `s^(-1)` and `15 m s^(-1)`, respectively
B. 6.5 m `s^(-1)` and 8 m `s^(- 1)`, respectively
C. 8.5 m `s^(-1)` and 13 m `s^(-1)`, respectively
D. 10.5 m `s^(-1)` and 15 m `s^(-1)`, respectively.

Answer

A

Explanation

When four coaches (m each) are attached with an engine (2m ), according to question power of engine `P=(4m+2m)` gv
if the engine pulls 12 coaches, power, `P=(12+2) mgv_(1)`
As the power of the engine · remains same, so `6mgv= 14 mgv_(1)`
`rArr v_(1) = (6)/(14) xx v rArr (6)/(14) xx 20 = (6 xx 10)/( 7) = (60)/(7)`
`rArr v_(1) = 8.5 m s^(-1)`
Similarly, for six coaches
`6 mgv=8mgv_(2)`
`rArr v_(2) = (6)/(8) xx 20 = (3)/(4) xx 20 = 15 m s^(-1)`.