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. (a) `8.5ms^-1` and `15ms^-1`, respectively
B. (b) `6.5ms^-1` and `8ms^-1`, respectively
C. (c) `8.5ms^-1` and `13ms^-1` respectively
D. (d) `10.5ms^-1` and `15ms^-1`, respectively

Answer

A

Explanation

When four coaches (m each) are attached with an engine `(2m)`,
according to question
`P=K6mgv` (i)
(Costant powr, K being proportionality constant)
Since resistive force is proportional to weight,
if 12 coaches are attached
`P=K 14mgv_1` (ii)
So by Eqs. (i) and (ii), `5mgv=14mgv_1`
`v_1=6/14xxv`
`6/14xx20=(6xx10)/(7)=60/7`
`v_1=S8.5ms^-1`
Similarly, for six coaches
`K6mgv=k8mgv_2`
`v_2=6/8xx20=3/4xx20=3/4xx20=15ms^-1`