Question:
A car is moving along a straight horizontal road with a speed \(v_0\). If the coefficient of friction between the tyres and the road is \(\mu\), the shortest distance in which the car can be stopped is
A car is moving along a straight horizontal road with a speed \(v_0\). If the coefficient of friction between the tyres and the road is \(\mu\), the shortest distance in which the car can be stopped is
Show Hint
Stopping distance is independent of mass of the car.
Updated On: Apr 23, 2026
- \(\frac{v_0^2}{\mu g}\)
- \(\left(\frac{v_0}{\mu g}\right)^2\)
- \(\frac{v_0^2}{\mu g}\)
- \(\frac{v_0^2}{2\mu g}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Work done by friction = Change in kinetic energy. Friction force \(f = \mu mg\).
Step 2: Detailed Explanation:
Initial KE = \(\frac{1}{2}mv_0^2\). Work done by friction = \(f \cdot s = \mu mg \cdot s\).
Equating: \(\frac{1}{2}mv_0^2 = \mu mg s \Rightarrow s = \frac{v_0^2}{2\mu g}\).
Step 3: Final Answer:
Thus, shortest stopping distance = \(\frac{v_0^2}{2\mu g}\).
Work done by friction = Change in kinetic energy. Friction force \(f = \mu mg\).
Step 2: Detailed Explanation:
Initial KE = \(\frac{1}{2}mv_0^2\). Work done by friction = \(f \cdot s = \mu mg \cdot s\).
Equating: \(\frac{1}{2}mv_0^2 = \mu mg s \Rightarrow s = \frac{v_0^2}{2\mu g}\).
Step 3: Final Answer:
Thus, shortest stopping distance = \(\frac{v_0^2}{2\mu g}\).
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET Magnetic Force Questions
- The magnetic field at the center of a circular current-carrying loop of radius $R$ is $B$. The field at a point on the axis at a distance $R$ from the center is:
- The magnetic moment of a transition metal ion is \( \sqrt{15} \,\text{BM} \). Therefore, the number of unpaired electrons present in it is
- A copper wire of diameter 1.6 mm carries a current I. The maximum magnetic field due to this wire is \(5 \times 10^{-4} \, T\). The value of I is :
- The force per unit length between two parallel current carrying straight conductors separated by \(2d\) is given by the formula:
- Two parallel conductors A and B of equal length carry currents i and 10 i, respectively, in the same direction. Then
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions