Question:
A bead P sliding on a frictionless semi-circular string... bead Q ejected... relation between $t_P$ and $t_Q$ is
A bead P sliding on a frictionless semi-circular string... bead Q ejected... relation between $t_P$ and $t_Q$ is
Show Hint
Brachistochrone principle: Curved path under gravity is faster.
Updated On: Feb 24, 2026
- $t_P>t_Q$
- $t_P>1.25 t_Q$
- $t_P = t_Q$
- $t_P<t_Q$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Bead Q moves at constant speed $v$.
Bead P accelerates due to gravity on the curved path, so average speed $> v$.
Despite longer path, the increased speed results in shorter time.
Bead P accelerates due to gravity on the curved path, so average speed $> v$.
Despite longer path, the increased speed results in shorter time.
Was this answer helpful?
1
0
Top Questions on Kinematics
- The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (\(R \le L\)) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :
- JEE Main - 2026
- Physics
- Kinematics
Acceleration-time (\(a-t\)) graph of a body is shown. The corresponding velocity-time (\(v-t\)) graph is
- WBJEE - 2026
- Physics
- Kinematics
- Water drops fall from a tap on the floor, \(5\) m below, at regular intervals of time. The first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from the ground, at the instant when the first drop strikes the ground, is ________ m. (\( g = 10 \, \text{m s}^{-2} \))
- JEE Main - 2026
- Physics
- Kinematics
- Paratrooper jumps... opens parachute after 2s... initial height is ___ m.
- JEE Main - 2026
- Physics
- Kinematics
- The r.m.s. speed of oxygen molecules at 47 $^\circ$C is equal to that of the hydrogen molecules kept at _________ $^\circ$C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)}
- JEE Main - 2026
- Physics
- Kinematics
View More Questions
Questions Asked in JEE Main exam
- Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors such that \[ \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}). \] If \( |\vec{a}| = 1 \), \( |\vec{b}| = 4 \), \( |\vec{c}| = 2 \), and the angle between \( \vec{b} \) and \( \vec{c} \) is \(60^\circ\), then \( |\vec{a} \cdot \vec{c}| \) is equal to.
- JEE Main - 2026
- Vector Algebra
- A thin convex lens of focal length \( 5 \) cm and a thin concave lens of focal length \( 4 \) cm are combined together (without any gap), and this combination has magnification \( m_1 \) when an object is placed \( 10 \) cm before the convex lens.
Keeping the positions of the convex lens and the object undisturbed, a gap of \( 1 \) cm is introduced between the lenses by moving the concave lens away. This leads to a change in magnification of the total lens system to \( m_2 \).
The value of \( \dfrac{m_1}{m_2} \) is
- For the matrices \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} -29 & 49 \\ -13 & 18 \end{bmatrix} \), if \( (A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} \), then among the following which one is true?}
- JEE Main - 2026
- Matrices
- A collimated beam of light of diameter 2 mm is propagating along the x-axis. The beam is required to be expanded into a collimated beam of diameter 14 mm using a system of two convex lenses. If the first lens has focal length 40 mm, then the focal length of the second lens is_____ mm.
- JEE Main - 2026
- Ray optics and optical instruments
- In a microscope, the objective has a focal length \(f_o=2\) cm and the eye-piece has a focal length \(f_e=4\) cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is_____.
- JEE Main - 2026
- Ray optics and optical instruments
View More Questions