Particles of masses m, 2m, 3m, dots, nm grams | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The position of the centre of mass $X_{CM}$ is given by the formula:$X_{CM} = \frac{\sum m_i x_i}{\sum m_i}$Substituting the given values:$X_{CM}

Vedclass · Accepted Answer

$\frac{(2n + 1)l}{3}$

Vedclass · Answer

(A) The position of the centre of mass $X_{CM}$ is given by the formula:$X_{CM} = \frac{\sum m_i x_i}{\sum m_i}$Substituting the given values:$X_{CM} = \frac{m(l) + 2m(2l) + 3m(3l) + \dots + nm(nl)}{m + 2m + 3m + \dots + nm}$Factoring out $m$ and $l$:$X_{CM} = \frac{ml(1^2 + 2^2 + 3^2 + \dots + n^2)}{m(1 + 2 + 3 + \dots + n)}$Using the standard summation formulas $\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$ and $\sum_{k=1}^n k = \frac{n(n+1)}{2}$:$X_{CM} = \frac{l \cdot \frac{n(n+1)(2n+1)}{6}}{\frac{n(n+1)}{2}}$Simplifying the expression:$X_{CM} = l \cdot \frac{n(n+1)(2n+1)}{6} \cdot \frac{2}{n(n+1)}$$X_{CM} = \frac{(2n+1)l}{3}$

Particles of masses $m, 2m, 3m, \dots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \dots, nl$ cm from a fixed point. The distance of the centre of mass of the particles from the fixed point (in cm) is

Similar Questions

Systematics refers to the

$A$ simple harmonic progressive wave is given by $y = y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $\left(\frac{1}{8}\right)^{\text{th}}$ of the maximum particle velocity,then the wavelength is:

$A$ thin uniform,circular ring is rolling down an inclined plane of inclination $30^\circ$ without slipping. Its linear acceleration along the inclined plane will be

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

Which of the following is considered an acellular organism?

Vedclass Test Series

Exam Paper Generator

Online Exam Module