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 and 15 m/s respectively
B. 6.5 m/s and 8 m/s respectively
C. 8.5 m/s and 13 m/s respectively
D. 10.5 m/s and 15 m/s respectively

Answer

A

Explanation

When 4 coaches (m each) are attached with engine (2m) according to question `P=K6mgv`
(constant power),(Kbeing proportionality constant) Since resistive force is proportional to weight
Now is 12 coaches are attached
`P=K14mgv^1`
So by equation (1) and (2)
`6mgv=14mgv_1`
`v_1=(6)/(14)xxV`
`implies=(6)/(14)xx20=(6xx10)/(7)=(60)/(7)`
`=v_1=8.5(m)/(sec)`
Similarly for 6 coaches
`impliesK6mgv=K8mgv_2`
`impliesv_2=(6)/(8)xx20=(3)/(4)xx20=15(m)/(sec)`