Question:
Two balls, having linear momenta $ \rho_1 = p \widehat{i} $ and $\rho_2 = - p \widehat{i}, $ undergo a collision in free space. There is no external force acting on the balls. Let $ \rho_2 ' \, and \, \rho_2 ' $. be their final momenta. The following option figure (s) is (are) not allowed for any non-zero value of $ \rho, a_1, a_2, b_1, b_2, c_1 \, and c_2$.
Two balls, having linear momenta $ \rho_1 = p \widehat{i} $ and $\rho_2 = - p \widehat{i}, $ undergo a collision in free space. There is no external force acting on the balls. Let $ \rho_2 ' \, and \, \rho_2 ' $. be their final momenta. The following option figure (s) is (are) not allowed for any non-zero value of $ \rho, a_1, a_2, b_1, b_2, c_1 \, and c_2$.
Updated On: Jun 14, 2022
- $ \rho_1' = a_1 \widehat{ i } + b_1 \widehat{ j} + c_1 \widehat{k}, \rho_2 = a_2 \widehat{ i } + b_2 \widehat{ j} $
- $ \rho_1 ' = c_1 \widehat{ k} , \rho_2 = c_2 \widehat{ k} $
- $ \rho_1' = a_1 \widehat{ a_1 } \widehat{ i} + b_1 \widehat{ j } + c_1 \widehat{k} , \rho_2 = a_2 \widehat{ i } + b_2 \widehat{ j} - c_1 \widehat{ k} $
- $ \rho_1 ' = a_1 \widehat{i} + b_1 \widehat{j} + c_1 \widehat{k}, \rho_2 = a_2 \widehat{i} + b_1 \widehat{j}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Initial momentum of the system $ \rho_1 + \rho_2 = 0 $
$\therefore$ Final momentum $ \rho_1 ' + \rho_2 ' $ should also be zero
Option (b) is allowed because if we put $ c_1 = - c_2 \ne 0, $
$ \rho_1 ' + \rho_2 ' $ W'H t>e zero. Similary, we can check other options.
$\therefore$ Correct options are (a) and (d).
$\therefore$ Final momentum $ \rho_1 ' + \rho_2 ' $ should also be zero
Option (b) is allowed because if we put $ c_1 = - c_2 \ne 0, $
$ \rho_1 ' + \rho_2 ' $ W'H t>e zero. Similary, we can check other options.
$\therefore$ Correct options are (a) and (d).
Was this answer helpful?
0
0
Top Questions on System of Particles & Rotational Motion
- During an elastic collision between two bodies, which of the following statements are correct?
- KCET - 2025
- Physics
- System of Particles & Rotational Motion
- The temperature of a body in air falls from \( 40^\circ \text{C} \) to \( 24^\circ \text{C} \) in 4 minutes. The temperature of the air is \( 16^\circ \text{C} \). The temperature of the body in the next 4 minutes will be:
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is \( n \) times higher than the moment of inertia of the given ring. Here, \( n = \):
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
View More Questions
Questions Asked in JEE Advanced exam
- A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field 𝐵⃗ pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height 𝐿, is placed in the x-y plane with its vertex P at x = 0 in the orientation shown in the figure. At 𝑡 = 0, the loop starts entering the region of the magnetic field with a uniform velocity 𝑣 along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graph best depicts the variation of the induced emf (E) in the loop as a function of the distance (𝑥) starting from 𝑥 = 0? - An organic compound P having molecular formula C6H6O3 gives ferric chloride test and does not have intramolecular hydrogen bond. The compound P reacts with 3 equivalents of NH2OH to produce oxime Q. Treatment of P with excess methyl iodide in the presence of KOH produces compound R as the major product. Reaction of R with excess iso-butylmagnesium bromide followed by treatment with H3O+ gives compound S as the major product.
The total number of methyl (−CH3) group(s) in compound S is ____.- JEE Advanced - 2024
- Aldehydes, Ketones and Carboxylic Acids
- Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ \(\epsilon_0 \)is the permittivity of free space.]
- JEE Advanced - 2024
- Moving charges and magnetism
- Let R2 denote R × R. Let
S = {(a, b, c) : a, b, c ∈ R and ax2 + 2bxy + cy2 > 0 for all (x, y) ∈ R2 - {(0, 0}}.
Then which of the following statements is (are) TRUE ?- JEE Advanced - 2024
- Quadratic Equations
- An aqueous solution of hydrazine (N2H4) is electrochemically oxidized by O2, thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is N2(g).
Choose the correct statement(s) about the above process- JEE Advanced - 2024
- Electrochemistry
View More Questions
Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.