MHT CET · Physics · Center of Mass Momentum and Collision
Three identical metal balls each of radius ' \(r\) ' are placed such that an equilateral triangle is formed when centres of three ball are joined. The centre of mass of the system is located at
- A centre of one of the balls.
- B point of intersection of medians.
- C line joining centres of any two balls.
- D on the circumference of any one of the balls.
Answer & Solution
Correct Answer
(B) point of intersection of medians.
Step-by-step Solution
Detailed explanation
Balls are identical and of same radius, so volume and density of balls are the same.
\(\therefore \quad\) Masses of the ball will be same
\(\begin{aligned}
& \mathrm{X}_{\mathrm{cm}}=\frac{\mathrm{mx}_1+\mathrm{mx}_2+\mathrm{mx}_3}{\mathrm{~m}+\mathrm{m}+\mathrm{m}}=\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{3} \\
& \mathrm{Y}_{\mathrm{cm}}=\frac{\mathrm{my}_1+\mathrm{my}_2+\mathrm{my}_3}{\mathrm{~m}+\mathrm{m}+\mathrm{m}}=\frac{\mathrm{y}_1+\mathrm{y}_2+\mathrm{y}_3}{3}
\end{aligned}\)
\(\mathrm{X}_{\mathrm{cm}}, \mathrm{Y}_{\mathrm{cm}}\) is the centroid of the equilateral triangle.
\(\therefore \quad\) Masses of the ball will be same
\(\begin{aligned}
& \mathrm{X}_{\mathrm{cm}}=\frac{\mathrm{mx}_1+\mathrm{mx}_2+\mathrm{mx}_3}{\mathrm{~m}+\mathrm{m}+\mathrm{m}}=\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{3} \\
& \mathrm{Y}_{\mathrm{cm}}=\frac{\mathrm{my}_1+\mathrm{my}_2+\mathrm{my}_3}{\mathrm{~m}+\mathrm{m}+\mathrm{m}}=\frac{\mathrm{y}_1+\mathrm{y}_2+\mathrm{y}_3}{3}
\end{aligned}\)
\(\mathrm{X}_{\mathrm{cm}}, \mathrm{Y}_{\mathrm{cm}}\) is the centroid of the equilateral triangle.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A coil of ' n ' turns and area ' A ' is suddenly removed from a magnetic field, a charge ' \(q\) ' flows through the coil. If resistance of the coil is ' \(R\) ' then the magnetic flux density is (in \(\mathrm{Wb} / \mathrm{m}^2\) )MHT CET 2025 Medium
- If coil is open then \(L\) and \(R\) becomeMHT CET 2007 Hard
- A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the e.m.f of the battery. The ratio of the energy stored in the capacitor to the work done by the battery will beMHT CET 2021 Easy
- The time period a satellite of earth is 5 hours. If the separation between the earth and the satellite in increased to four times the previous value, the new time period of the satellite will beMHT CET 2021 Easy
- The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight isMHT CET 2012 Medium
- A gardening pipe having an internal radius ' \(R\) ' is connected to a water sprinkler having ' \(n\) ' holes each of radius ' \(r\) '. The water in the pipe has a speed ' \(v\) '. The speed of water leaving the sprinkler isMHT CET 2024 Medium
More PYQs from MHT CET
- The increasing order of reactivity of alkaline earth metals with water isMHT CET 2020 Easy
- Calculate molality of solution of a nonvolatile solute having boiling point elevation \(1.89 \mathrm{~K}\) if boiling point elevation constant of solvent is \(3.15 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\).MHT CET 2023 Easy
- A source of sound is moving towards a stationary observer with \(\left(\frac{1}{10}\right)^{\text {th }}\) the of the speed of sound. The ratio of apparent to real frequency isMHT CET 2023 Hard
- If the . (cumulative distribution function) is given by then ________MHT CET 2019 Hard
- On the interval \([0,1]\) the function \(x^{25}(1-x)^{75}\) takes its maximum value at the pointMHT CET 2007 Medium
- In the processing of hnRNA in eukaryotic cell, the primary transcripts are processed in the following sequence.MHT CET 2024 Medium