Circular Motion

Q: A point mass $m$ attached to a massless string is undergoing circular motion in a vertical plane. Th...

The point in a vertical circular motion with the least tension will be the top point. Meanwhile, the point with maximum speed will be the bottom point. The FBD can be made as shown.Using the above FBD:$$ \begin{gathered} \frac{m v^2}{R}=T+m g \\ \frac{m v^2}{R}=2 m g+m g=3 m g \\ v_{\text {top }}=\sqrt{3 R g} \end{gathered} $$Now, using TME on the top and bottom points:$$ \frac{1}{2} m v_{t o p}^2+m g h=\frac{1}{2} m v_{\max }^2 $$Here, $h$ will be the difference in the height between the two points $(2 R)$ and you can cancel out $m$ from all the terms$$ \begin{gathered} \frac{1}{2}(3 R g)+2 R g=\frac{1}{2}\left(v_{\max }^2\right) \\ v_{\max }^2=3 R g+4 R g=7 R g \\ v_{\max }=\sqrt{7 R g} \end{gathered} $$

Q: On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a poin...

In this scenario, two cyclists, Abhijit and Vani, set off from the same point on a circular track in opposite directions. Abhijit rides at a constant speed, while Vani accelerates from rest. They meet again on the track when their speeds are equal. Here's the analysis:Abhijit's constant speed is $ v_1 $.Vani's speed when they meet is $ v_2 $.Vani's acceleration is $ a $.As Abhijit travels at a constant speed, the distance he covers, $ d_1 $, is given by:$ d_1 = v_1 \cdot t $Vani, starting from rest and accelerating uniformly, reaches a speed $ v_2 $ when they meet, which is calculated by:$ v_2 = a \cdot t $The distance $ d_2 $ that Vani travels, using the equation for uniformly accelerated motion, is:$ d_2 = \frac{1}{2} a t^2 $Since Abhijit and Vani meet with the same speed:$ v_1 = v_2 = a \cdot t $This implies:$ a = \frac{v_1}{t} $Substituting this expression for $ a $ back into Vani's distance equation gives:$ d_2 = \frac{1}{2} \left(\frac{v_1}{t}\right) t^2 $$ d_2 = \frac{1}{2} v_1 \cdot t $Thus, we have:Abhijit's distance: $ d_1 = v_1 \cdot t $Vani's distance: $ d_2 = \frac{1}{2} v_1 \cdot t $Therefore:$ d_1 = 2 \cdot d_2 $This means Abhijit traveled double the distance traveled by Vani.

PYQ 2022

hard

physics ID: iat-iise

A point mass attached to a massless string is undergoing circular motion in a vertical plane. The length of the string is and the acceleration due to gravity is . If the minimum value of the tension in the string is 2 mg , the maximum speed of this circular motion of the point mass is

PYQ 2024

medium

physics ID: iat-iise

On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves with a constant speed. Vani starts with a constant acceleration from rest. They meet again on the track with the same speed. Which of the following is correct?

Abhijit travelled the same distance travelled by Vani.

Abhijit travelled half the distance travelled by Vani.

Abhijit travelled double the distance travelled by Vani.

Abhijit travelled of the distance travelled by Vani.

High-Yield Trend

Questions
2 MCQs

Official Solution

Official Solution

Circular Motion

High-Yield Trend

Questions 2 MCQs

Official Solution

Official Solution

Questions
2 MCQs