Respuesta :
Answer:
The ratio of the power generated by the engines are [tex]\dfrac{2}{3}[/tex]
(b) is correct option.
Explanation:
Given that,
Mass of Tesla = 2000 Kg
Torque = 400 Nm
Mass of Mercedes = 1.5 M Tesla
The Benz engine produces 50% more torque than the Tesla.
We need to calculate the power generated by the engines 6 seconds after a start from rest
Using formula of power
[tex]P=F\cdot v[/tex]
We know that,
[tex]v=at[/tex]
[tex]v=\dfrac{F}{m}t[/tex]
[tex]v=\dfrac{\tau}{mr}t[/tex]
Put the value of F and v in equation (I)
[tex]P=\dfrac{\tau}{r}\times\dfrac{\tau}{mr}t[/tex]
[tex]P=\dfrac{\tau^2t}{mr^2}[/tex]
Here, r and t are same for both bodies.
[tex]P\propto\dfrac{\tau^2}{m}[/tex]
We need to calculate the ratio of the power generated by the engines
Using formula of power
[tex]\dfrac{P_{T}}{P_{B}}=\dfrac{\tau_{T}^2}{m_{T}}\times\dfrac{m_{B}}{\tau_{B}}[/tex]
Put the value into the formula
[tex]\dfrac{P_{T}}{P_{B}}=\dfrac{400^2}{2000}\times\dfrac{3000}{600^2}[/tex]
[tex]\dfrac{P_{T}}{P_{B}}=\dfrac{2}{3}[/tex]
Hence, The ratio of the power generated by the engines are [tex]\dfrac{2}{3}[/tex]
