Question:
Consider a disc rotating in the horizontal plane with a constant angular speed to about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) \(\omega\) remains constant throughout. Then
Consider a disc rotating in the horizontal plane with a constant angular speed to about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) \(\omega\) remains constant throughout. Then
Updated On: May 19, 2024
- P lands in the shaded region and Q in the un shaded region
- P lands in the unshaded region and Q in the shaded region
- both P and Q land in the unshaded region
- both P and Q land in the shaded region
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Since the disc completes \(\frac{1}{8}\) of a rotation, the time for \(\frac{1}{8}\) rotation is \(\frac{T}{8}\), where T is the period of the disc.
The period T is given by \(T=\frac{2\pi}{\omega}\)
Therefore, the time for 1/8 rotation is \(t = \frac{T}{8} = \frac{2\pi}{8\omega} = \frac{\pi}{4\omega}\)
X- coordinate of P = ωRt
\(= \frac{πR}{4} \gt Rcos45\degree\)
Therefore, P and Q lands in the unshaded region.
So. the correct option is (D): both P and Q land in the shaded region
Was this answer helpful?
0
1
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 \(P\) with molecular formula \(C_6H_6O_3\) gives a ferric chloride test and does not have an intramolecular hydrogen bond. The compound \(P\) reacts with 3 equivalents of \(NH_2OH\) 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 \(H_3O^+\) gives compound \(S\) as the major product. The total number of methyl (\(-CH_3\)) groups in compound \(S\) is \_\_\_\_\_.
- JEE Advanced - 2024
- Qualitative Analysis
- 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
- Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other.
[en = H2NCH2CH2NH2]- JEE Advanced - 2024
- coordination compounds
- Among the following complexes, the total number of diamagnetic species is ______.
[Mn(NH3)6]3+, [MnCl6]3−, [FeF6]3−, [CoF6]3−, [Fe(NH3)6]3+, and [Co(en)3]3+
[Given, atomic number: Mn = 25, Fe = 26, Co = 27;
en = H2NCH2CH2NH2]- JEE Advanced - 2024
- coordination compounds
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.