If the car is moving on the level road at a speed of 50 km/h has a wheelbase 4 m, a distance of C. G. from ground 800 mm and distance from rear wheels is 1.2 m. Coefficient of friction is 0.8. What is the retardation if the brakes are applied to the front wheels?

Solution (By Examveda Team)

$$ \begin{aligned} \textbf{Given:}\;& L=4\,\text{m},\; h=0.8\,\text{m},\; d_{\text{rear}}=1.2\,\text{m},\; \mu=0.8 \\[4pt] \text{Front axle distance:}\;& L-d_{\text{rear}}=2.8\,\text{m} \\[6pt] \textbf{Concept:}\;& \text{Front-wheel braking; force limited by front-axle load} \\[6pt] \text{Static front-axle load:}\;& W_f=W\frac{d_{\text{rear}}}{L}=0.3W \\[4pt] \text{Max braking force:}\;& F_{\max}=\mu W_f=0.3\mu W \\[4pt] \text{Retardation:}\;& a=\frac{F_{\max}}{m}=0.3\mu g \\[4pt] & a=0.8\times0.3\times9.81\approx2.35\,\text{m/s}^2\approx2.4\,\text{m/s}^2 \\[6pt] & \boxed{\text{Answer: } 2.4\,\text{m/s}^2\;(\text{Option B})} \end{aligned} $$