SATHEE: Rotational Motion Question 57

Rotational Motion Question 57

Question: Three particles, each of mass m grams situated at the vertices of an equilateral triangle ABC of side 1 cm . The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram $- c m^{2}$ units will be:

[AIPMT (S) 2004]

Options:

A) $(3 / 4) m l^{2}$

B) $2 m l^{2}$

C) $(5 / 4) m l^{2}$

D) $(3 / 2) m l^{2}$

Show Answer

Answer:

Correct Answer: C

Solution:

Moment of inertia of the system about AX is given by

$M I = m_{A} r_{A}^{2} + m_{B} r_{B}^{2} + m_{C} r_{C}^{2}$

$M I = m {(0)}^{2} + m {(l)}^{2} + m {(l \sin 30^{0})}^{2}$

$= m l^{2} + \frac{m l^{2}}{4} = \frac{5}{4} m l^{2}$

Alternative: Moment of inertia of a system about a line OC perpendicular to AB, in the plane of ABC is

$I_{C O} = m \times 0 + m \times {(\frac{1}{2})}^{2} + m \times {(\frac{1}{2})}^{2}$

$∴$ $I_{C O} = \frac{m l^{2}}{4} + \frac{m l^{2}}{4} = \frac{m l^{2}}{2}$

According to parallel-axis theorem

$I_{A X} = I_{C O} + M x^{2}$

where $x =$ distance of $A X$ from CO, $M =$ total mass of system

$I_{A X} = \frac{m l^{2}}{2} + 3 m \times {(\frac{l}{2})}^{2}$

$I_{A X} = \frac{m l^{2}}{2} + \frac{3 m l^{2}}{4} = \frac{5}{4} m l^{2}$

Rotational Motion Question 57

Question: Three particles, each of mass m grams situated at the vertices of an equilateral triangle ABC of side 1 cm . The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram $- c m^{2}$ units will be:

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Rotational Motion Question 57

Question: Three particles, each of mass m grams situated at the vertices of an equilateral triangle ABC of side 1 cm . The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram −cm2 units will be:

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

Question: Three particles, each of mass m grams situated at the vertices of an equilateral triangle ABC of side 1 cm . The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram $- c m^{2}$ units will be: