Motion In Straight Line

Question

The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is

$\frac{3 cl + 2 D l^{2}}{3 (2 c + D l)}$

$\frac{2 cl + 3 D I^{2}}{2 (4 c + 8 I)}$

$\frac{2 cl + 3 {DI}^{2}}{3 (2 c + I)}$

$\frac{cl + {DI}^{2}}{2 (2 c + DI)}$

Solution

$\frac{3 cl + 2 D l^{2}}{3 (2 c + D l)}$

Let the cross-sectional area is $α$ . The mass of an element of length dx located at a distance x away from the left end is (C + Dx) $α$ dx. The x-coordinate of the centre of mass is given by

$X_{cm} = \frac{\int x cm}{\int dm}$

= $\frac{\int_{0}^{l} x (C + Dx) α dx}{\int_{0}^{l} (C + Dx) α dx}$

Where limit is from 0 to l.

= $\frac{C \frac{l^{2}}{2} + \frac{D l}{3}}{Cl + \frac{D l^{2}}{2}}$

X_cm = $\frac{3 CI + 2 {DI}^{2}}{3 (2 C + DI)}$

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

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Motion In Straight Line

The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is

$\frac{3 cl + 2 D l^{2}}{3 (2 c + D l)}$

$\frac{2 cl + 3 D I^{2}}{2 (4 c + 8 I)}$

$\frac{2 cl + 3 {DI}^{2}}{3 (2 c + I)}$

$\frac{cl + {DI}^{2}}{2 (2 c + DI)}$

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

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For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is 3 cl + 2 D l23 2c + D l 2 cl + 3D I22 4c + 8I 2 cl + 3 DI23 2c + I cl + DI22 2 c + DI

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: (a) A kite flying in the sky. (b) The earth revolving around the sun. (c) A train moving along the equator of the earth in clockwise direction. (d) Accelerated motion of a particle in a straight line.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is

$\frac{3 cl + 2 D l^{2}}{3 (2 c + D l)}$

$\frac{2 cl + 3 D I^{2}}{2 (4 c + 8 I)}$

$\frac{2 cl + 3 {DI}^{2}}{3 (2 c + I)}$

$\frac{cl + {DI}^{2}}{2 (2 c + DI)}$

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.