MHT CET · Physics · Laws of Motion
A van is moving with a speed of \(108 \mathrm{~km} / \mathrm{hr}\) on a level road where the coefficient of friction between the tyres and the road is 0.5 . For the safe driving of the van, the minimum radius of curvature of the road shall be
(Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )
- A \(40 \mathrm{~m}\)
- B \(180 \mathrm{~m}\)
- C \(120 \mathrm{~m}\)
- D \(80 \mathrm{~m}\)
Answer & Solution
Correct Answer
(B) \(180 \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
The correct option is (B).
Concept: For safe driving, the centripetal force must be less than limiting friction otherwise the vehicle will skid away from the road.
Mathematically it can be written as
\(\frac{\mathrm{mv}}{\mathrm{r}} \leq \mu \mathrm{mg}\)
where \(m\) is the mass, \(v\) is the velocity, \(\mu\) is the coefficient of friction and \(g\) is the acceleration due to gravity.
On plugging the values given in the question,
\(r_{\min }=\frac{v^2}{\mu g}=\frac{30^2}{0.5 \times 10}=180 \mathrm{~m}\)
Concept: For safe driving, the centripetal force must be less than limiting friction otherwise the vehicle will skid away from the road.
Mathematically it can be written as
\(\frac{\mathrm{mv}}{\mathrm{r}} \leq \mu \mathrm{mg}\)
where \(m\) is the mass, \(v\) is the velocity, \(\mu\) is the coefficient of friction and \(g\) is the acceleration due to gravity.
On plugging the values given in the question,
\(r_{\min }=\frac{v^2}{\mu g}=\frac{30^2}{0.5 \times 10}=180 \mathrm{~m}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A coil has inductance 2H. The ratio of its reactance, when it is connected first to an AC source and then to DC source, isMHT CET 2019 Medium
- The kinetic energy of an electron is increased by 2 times, then the de-Broglie wavelength associated with it changes by a factor.MHT CET 2024 Hard
- In unbiased p-n junction diodeMHT CET 2025 Easy
- A photoelectric surface is illuminated successively by monochromatic light of Wavelength \(\lambda\) and \((\lambda / 3)\). If the maximum kinetic energy of the emitted photoelectrons in the second case is 4 times that in the first case, the work function of the surface of the material is ( \(\mathrm{h}=\) Planck's constant, \(\mathrm{c}=\) speed of light \()\)MHT CET 2024 Medium
- A particle moves along a circular path of radius \(r\) with uniform speed \(v\). The angle described by a particle in one second isMHT CET 2022 Easy
- A gardening pipe having an internal radius ' \(R\) ' is connected to a water sprinkler having ' \(n\) ' holes each of radius ' \(r\) '. The water in the pipe has a speed ' \(v\) '. The speed of water leaving the sprinkler isMHT CET 2024 Medium
More PYQs from MHT CET
- If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at \(47^{\circ} \mathrm{C}\), the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)MHT CET 2025 Medium
- The volume of a metal block increases by \(0.225 \%\) when its temperature is increased by \(30^{\circ} \mathrm{C}\). Hence coefficient of linear expansion of the material of metal block isMHT CET 2023 Medium
- Which among the following equations represents Arrhenius equation?MHT CET 2017 Medium
- Which of the following is not equal toMHT CET 2019 Easy
- Which among the following is haloalkyne?MHT CET 2023 Easy
- Two periodic waves of intensities \(I_{1}\) and \(I_{2}\) pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities isMHT CET 2008 Medium