JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A rod of length 5 L is bent right angle keeping one side length as 2 L.
The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))
- A \(2 \hat{i}+3 \hat{j}\)
- B \(3 \hat{i}+7 \hat{\mathrm{j}}\)
- C \(5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}\)
- D \(4 \hat{i}+9 \hat{j}\)
Answer & Solution
Correct Answer
(D) \(4 \hat{i}+9 \hat{j}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{x}_{\mathrm{com}}=\frac{2 \mathrm{~m}(10)+3 \mathrm{~m}(0)}{5 \mathrm{~m}}=4 \mathrm{~cm}\) \(\mathrm{y}_{\mathrm{com}}=\frac{2 \mathrm{~m}(0)+3 \mathrm{~m}(15)}{5 \mathrm{~m}}=9 \mathrm{~cm}\)…
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
- The output \(\mathrm{Y}\) of following circuit for given inputs is _______.
JEE Mains 2024 Hard - A bullet of mass \(5\, g\), travelling with a speed of \(210\) \(m / s ,\) strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is \(0.030\, cal /\left( g -{ }^{\circ} C \right)\) \(\left(1\, cal =4.2 \times 10^{7}\, ergs \right)\) close to\(.......^oC\)JEE Mains 2020 Medium
- Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :JEE Mains 2021 Hard
- Time period of a simple pendulum in a stationary lift is ' \(T\) '. If the lift accelerates with \(\frac{ g }{6}\) vertically upwards then the time period will be ..... (where \(g =\) acceleration due to gravity)JEE Mains 2022 Medium
- From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
(take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)
JEE Mains 2026 Hard - A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y\left( {x,t} \right) = 0.5\sin\, \left( {\frac{{5\pi }}{4}x} \right)\,\cos\, \left( {200\,\pi t} \right)\). What is the speed of the travelling wave moving in the positive \(x\) direction .... \(m/s\) ? (\(x\) and \(t\) are in meter and second, respectively.)JEE Mains 2017 Hard
More PYQs from JEE Mains
- The value of the integral \(\int\limits_4^{10} {\frac{{\left[ {{x^2}} \right]dx}}{{\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}}\) , where \(\left[ x \right]\) denotes the greatest integer less than or equal to \(x\), isJEE Mains 2016 Hard
- In the following circuit, the switch \(S\) is closed at \(t = 0.\) The charge on the capacitor \(C_1\) as a function of time will be given by \(\left( {{C_{eq}}\, = {\kern 1pt} \,\frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).\)
JEE Mains 2018 Hard - A body of mass \(2\, {kg}\) moving with a speed of \(4\, {m} / {s}\). makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is \(\frac{x}{10} \,{m} / {s}\). Then the value of \(x\) is ..... .JEE Mains 2021 Hard
- Given below are two statements: Statement \(I:\) For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement \(II:\) Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer from the options given below on :JEE Mains 2023 Medium
- If \(f(x)=\left\{\begin{array}{ccc}\frac{1}{|x|} & ; & |x| \geq 1 \\ a x^{2}+b & ; & |x|<1\end{array}\right.\) is differentiable at every point of the domain, then the values of \(a\) and \(b\) are respectivelyJEE Mains 2021 Hard
- Two particles having masses \(4\, g\) and \(16\, g\) respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is \(n : 2 .\) The value of \(n\) will be ...... .JEE Mains 2021 Medium