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The velocity of the center of mass ($V$) of a system of particles is related to the total linear momentum ($P$) and total mass ($M$) of the system by:
The NCERT summary mentions: 'Velocity of the centre of mass of a system of particles is given by $V = P/M$, where $P$ is the linear momentum of the system.'
Consider a system of two particles with masses $m_1$ and $m_2$ at positions $x_1$ and $x_2$ respectively along the x-axis. The position of their center of mass ($X_{CM}$) is given by:
For a two-particle system, the general formula $R = \frac{1}{M} \sum m_i r_i$ simplifies to $X_{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$ for coordinates along a single axis. This is consistent with the initial discussion on the center of mass in the NCERT text.
Which of the following is NOT a characteristic of pure translational motion of a rigid body?
In pure translation, according to the NCERT text and Figure 6.6(a), 'at any instant the velocities of any particles like O [center of mass] and P of the body are the same in pure translation.' Thus, option 4 describes a characteristic of combined translational and rotational motion, not pure translation.
Myasthenia gravis is an autoimmune disorder that primarily affects which part of the neuromuscular system?
The NCERT text states: 'Myasthenia gravis: Auto immune disorder affecting neuromuscular junction leading to fatigue, weakening and paralysis of skeletal muscle.'
Which of the following disorders is characterized by progressive degeneration of skeletal muscle and is mostly due to a genetic defect?
According to the NCERT context, 'Muscular dystrophy: Progressive degeneration of skeletal muscle mostly due to genetic disorder.'
A patient presents with rapid spasms and wild contractions in their muscles. A potential underlying cause, as per the provided information, could be low levels of what in the body fluid?
The NCERT text states: 'Tetany: Rapid spasms (wild contractions) in muscle due to low Ca++ in body fluid.'
Osteoporosis is an age-related disorder. What are its defining characteristics?
The provided text defines: 'Osteoporosis: Age-related disorder characterised by decreased bone mass and increased chances of fractures.'
In females, decreased levels of which hormone are a common cause of osteoporosis?
The NCERT text mentions: 'Decreased levels of estrogen is a common cause [of osteoporosis].'
Gout is a disorder characterized by the inflammation of joints. What substance accumulates in the joints to cause this inflammation?
The NCERT text clearly states: 'Gout: Inflammation of joints due to accumulation of uric acid crystals.'
Which of the following disorders involves inflammation of joints?
The NCERT definition for arthritis is 'Arthritis: Inflammation of joints.'
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