Conceptual Questions - Chapter 5 Motion of System of Particles and Rigid Bodies 11th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Conceptual Questions
Question 1.
When a tree is cut, the cut is made on the side facing the direction in which the tree is required to fall. Why?
Answer:
A cut on the tree is made on the side facing the direction in which the tree is required to fall because that side will no longer be supported by the normal force from the bottom, therefore the gravitational force tries to rotate it. So the torque given by the gravity to the tree makes the tree fall on the side as anticipated.
Question 2.
Why does a porter bend forward while carrying a sack of rice on his back?
Answer:
When a porter carries a sack of rice, the line of action of his center of gravity will go away from the body. It affects the balance, to avoid this he bends. By which center of gravity will realign within the body again. So balance is maintained.
Question 3.
Why is it much easier to balance a meter scale on your finger tip than balancing on a match stick? Answer:
A meter scale is larger then a match stick. So the center of gravity for meter scale is higher than a matchstick when we keep it vertically. It is easier to balance the object whose center of gravity is higher than the object whose centro of gravity is lower. So, it is hard to balance a match stick than a meter scale.

Question 4.
Two identical water bottles one empty and the other filled with water are allowed to roll down an inclined plane. Which one of them reaches the bottom first? Explain your answer.
Answer:
Mass of the empty water bottle mostly concentrated on its surface. So moment of inertia of empty water bottle is more than the bottle filled with water. As we know, moment of inertia is inversely proportional to angular velocity. Therefore, the bottle filled with water whirls with greater speed and reaches the ground first.
Question 5.
Write the relation between angular momentum and rotational kinetic energy. Draw a graph for the same. For two objects of same angular momentum, compare the moment of inertia using the graph.
Answer:
Let a rigid body of moment of inertia I rotate with angular velocity $\omega$.
The angular momentum of a rigid body is, $\mathrm{L}=\mathrm{I} \omega$
The rotational kinetic energy of the rigid body is, $\mathrm{KE}=\frac{1}{2} \mathrm{I} \omega^2$.
By multiplying the numerator and denominator of the above equation with I, we get a relation between $\mathrm{L}$ and $\mathrm{KE}$ as,
$
\begin{gathered}
\mathrm{KE}=\frac{1}{2} \frac{\mathrm{I}^2 \omega^2}{\mathrm{I}}=\frac{1}{2} \frac{(\mathrm{I} \omega)^2}{\mathrm{I}} \\
\mathrm{KE}=\frac{\mathrm{L}^2}{2 \mathrm{I}} \\
\text { As } \mathrm{KE}=\frac{\mathrm{L}^2}{2 \mathrm{I}} \text { i.e. } \mathrm{KE} \propto \mathrm{L}^2 .
\end{gathered}
$
It resembles with $\mathrm{y}=\mathrm{Kx}^2$. If angular momentum is same for two objects, kinetic energy is inversely proportional to moment of inertia.
Moment of inertia of the object whose kinetic energy is lesser will have greater magnitude.
Question 6.
Three identical solid spheres move down through three inclined planes A, B and $\mathrm{C}$ all same dimensions. $\mathrm{A}$ is without friction, $\mathrm{B}$ is undergoing pure rolling and $\mathrm{C}$ is rolling with slipping. Compare the kinetic energies $\mathrm{E}_{\mathrm{A}}, \mathrm{E}_{\mathrm{B}}$ and $\mathrm{E}_{\mathrm{C}}$ at the bottom.
Answer:
Even though, the three identical solid spheres of same dimensions move down through three different inclined plane, according to the law of conservation of energy, the potential energy possessed by these three solid spheres will be converted into kinetic energies. So the kinetic energies $\mathrm{E}_{\mathrm{A}}, \mathrm{E}_{\mathrm{B}}$ and $\mathrm{E}_{\mathrm{C}}$ are equal at the bottom.
Question 7.
Give an example to show that the following statement is false. Any two forces acting on a body can be combined into single force that would have same effect.
Answer:

A single force i.e. resultant of two forces acting on a body depends upon the angle between them also. The simple example for this is if two forces $5 \mathrm{~N}$ and $5 \mathrm{~N}$ acting on the object in the opposite direction, the single resultant force acting on the body is zero. But, if two forces acting on the
object along the same direction, then the resultant i.e. the single force is $5+5=10 \mathrm{~N}$. Hence the given statement "any two forces acting on a body can be combined into single force that would leave same effect" is wrong.