Question

science students plz help with physics... :(​

Answer 1

Question - 1 :

Consider a system of two particles having masses m₁ and m₂. If the particle of mass m₁ is pushed towards the centre of mass of particles through a distance d, by what distance would the particle of mass m₂ move so as to keep the mass centre of particles at the original position.

Solution :

The system of two given particles of masses m₁ and m₂ are shown in figure.

m₁ ⬤------(r₁)------•------(r₂)------⬤ m₂

Initially the centre of mass

$\implies\sf\:r_{CM}=\dfrac{m_1r_1+m_2r_2}{m_1+m_2}$

When mass 1 moves towards centre of mass by a distance d, then let mass 2 moves a distance d' away from CM to keep the CM in its initial position.

$\implies\sf\:r_{CM}=\dfrac{m_1(r_1-d)+m_2(r_2+d')}{m_1+m_2}$

Equating both equations, we get

$\implies\sf\:\dfrac{m_1r_1+m_2r_2}{m_1+m_2}=\dfrac{m_1(r_1-d)+m_2(r_2+d')}{m_1+m_2}$

$\implies\sf\:-m_1d+m_2d'=0$

$\implies\bf\:d'=\dfrac{m_1}{m_2}\:d$

Question - 2 :

O is the centre of an equilateral ∆ABC. F₁, F₂ and F₃ are three forces acting along the sides AB, BC and AC as shown in figure. What should be the magnitude of F₃, so that the total torque about O is zero?

Solution :

Let r be the perpendicular distance of F₁, F₂ and F₃ from O.

The torque of force F₃ about O is clockwise, while torque due to F₁ and F₂ are anti-clockwise.

For total torque to be zero about O, we must have

➝ F₁r + F₂r - F₃r = 0

➝ F₃ = F₁ + F₂

Answer 2

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