Question:
On imparting an initial velocity \(v_0\), a ball begins to move in horizontal circle of radius \(R\) on horizontal plane. If the coefficient of friction between the ball and plane is \(\mu\), then the time required by ball to come to rest is:
center
On imparting an initial velocity \(v_0\), a ball begins to move in horizontal circle of radius \(R\) on horizontal plane. If the coefficient of friction between the ball and plane is \(\mu\), then the time required by ball to come to rest is:
center
Show Hint
Whenever friction alone slows a body on a horizontal surface:
\[
a=\mu g
\]
This is one of the most important standard results in mechanics.
Updated On: Jun 17, 2026
- \(\dfrac{v_0^2}{\mu g}\)
- \(\dfrac{\mu g}{v_0}\)
- \(\dfrac{v_0\mu}{g}\)
- \(\dfrac{v_0}{\mu g}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
Friction opposes motion and produces retardation.
Frictional force:
\[
f=\mu N
\]
On a horizontal plane:
\[
N=mg
\]
Hence,
\[
f=\mu mg
\]
Retardation:
\[
a=\frac{f}{m}
\]
\[
=\mu g
\]
Since friction is constant, motion is uniformly retarded.
Using first equation of motion:
\[
v=u-at
\]
At stopping point:
\[
v=0
\]
Step 1: Apply equation of motion. \[ 0=v_0-\mu gt \] \[ \mu gt=v_0 \] \[ t=\frac{v_0}{\mu g} \] Therefore, \[ \boxed{\frac{v_0}{\mu g}} \]
Step 1: Apply equation of motion. \[ 0=v_0-\mu gt \] \[ \mu gt=v_0 \] \[ t=\frac{v_0}{\mu g} \] Therefore, \[ \boxed{\frac{v_0}{\mu g}} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Circular motion Questions
- A car is moving with a speed of 5 m/s on a circular road having radius of curvature 10 m and coefficient of friction 0.5. For the safe journey of the car, the banking angle of the road should be:
- A body of mass 10 g is tied to a string of length 0.4 m and it is whirled in a horizontal plane with a speed of 6 m/s. Then the tension in the string is
- A lorry is moving on a smooth circular path of radius 50 m with a velocity of 20 m/s. Then the banking angle of the road is:
- A bike race is conducted on a circular track of radius $60\text{ m}$. If the slowest bike, weighing $120\text{ kg}$, moved around the track at a constant speed of $108\text{ kmph}$, then the time taken by it to complete one lap and its acceleration are respectively
- A stone of mass $400\text{ g}$ tied to one end of a string is rotated in a horizontal circle of radius $125\text{ m}$. If the string can withstand a maximum tension of $50\pi^{2}\text{ N}$ then the minimum time period with which the stone can be rotated is
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions