Question:
An object is sliding from the top of the smooth inclined plane of height \( h \) from rest and it just completes a vertical circle of diameter 20 cm. Then the minimum height \( h \) of smooth inclined plane is:
An object is sliding from the top of the smooth inclined plane of height \( h \) from rest and it just completes a vertical circle of diameter 20 cm. Then the minimum height \( h \) of smooth inclined plane is:
Show Hint
For any object to complete a vertical circle, the required release height on a smooth incline is always \( 2.5 \) times the radius of the circle.
Updated On: Jun 9, 2026
- \( 0.25 \) m
- \( 0.2 \) m
- \( 0.5 \) m
- \( 2.5 \) m
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
For an object sliding down a smooth inclined plane and entering a loop-the-loop to complete a vertical circle, the conservation of energy dictates the minimum height. To barely complete the circle, the velocity at the top of the loop must be \( v_{top} = \sqrt{gr} \).
Step 1: State the energy conservation condition.
Using conservation of energy from the release height \(h\) to the top of the circle \(2r\): $$ mgh = mg(2r) + \frac{1}{2}m v_{top}^2 $$ $$ mgh = 2mgr + \frac{1}{2}m(gr) = 2.5mgr $$ $$ h = 2.5r = \frac{5}{2}r $$
Step 2: Convert diameter to radius.
Diameter \( D = 20 \) cm, so radius \( r = 10 \) cm \(= 0.1\) m.
Step 3: Calculate height.
$$ h = 2.5 \times 0.1 \text{ m} = 0.25 \text{ m} $$ $$\boxed{0.25 \text{ m}}$$
Step 1: State the energy conservation condition.
Using conservation of energy from the release height \(h\) to the top of the circle \(2r\): $$ mgh = mg(2r) + \frac{1}{2}m v_{top}^2 $$ $$ mgh = 2mgr + \frac{1}{2}m(gr) = 2.5mgr $$ $$ h = 2.5r = \frac{5}{2}r $$
Step 2: Convert diameter to radius.
Diameter \( D = 20 \) cm, so radius \( r = 10 \) cm \(= 0.1\) m.
Step 3: Calculate height.
$$ h = 2.5 \times 0.1 \text{ m} = 0.25 \text{ m} $$ $$\boxed{0.25 \text{ m}}$$
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 Work Power and Energy Questions
The acceleration of a particle which moves along the positive \( x \)-axis varies with its position as shown in the figure. If the velocity of the particle is \( 0.8 \, \text{m/s} \) at \( x = 0 \), then its velocity at \( x = 1.4 \, \text{m} \) is:
- A machine with efficiency \( \frac{2}{3} \) used 12 J of energy in lifting a 2 kg block through a certain height and it is allowed to fall through the same. The velocity while it reaches the ground is:
- The force, $F = (2x^2 + 5x + 4)$ N is acting on a body. If the body moves from $x = -1$ m to $x = +1$ m in the direction of force, then the work done by the force is
- The power of an engine which draws 1000 kg of water from a well of depth 9 m in one minute is (acceleration due to gravity $g = 10$ m/s$^2$)
- The work done in lifting a body of mass 2 kg from the surface of the earth to a height 10 m 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