A ball is released from a height of \(1\) \(m\) on a fixed smooth hemispherical surface as shown. Find its velocity when it is at a height of \(0.5\) \(m\) from ground. (take \(g\) = \(10\;m / s^2\))
- \(20 \;m/s\)
- \(10 \;m/s\)
- \(\sqrt{10}\; m/s\)
- \(5 \;m/s\)
The Correct Option is C
Solution and Explanation
The Correct Option is (C): \(\sqrt{10}\; m/s\)
Top Questions on speed and velocity
- Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:
- JEE Main - 2025
- Physics
- speed and velocity
A block of mass 2 kg is tied to one end of a 2 m long metal wire of 1.0 mm² area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is 2 mm, the Young's modulus of the metal is:
- TS EAMCET - 2024
- Physics
- speed and velocity
The velocity (v) - time (t) plot of the motion of a body is shown below :
The acceleration (a) - time(t) graph that best suits this motion is :- NEET (UG) - 2024
- Physics
- speed and velocity
- If a particle executing simple harmonic motion with period \( T \) and displacement \( x = A \cos(\omega t) \), then the acceleration and velocity of the particle at the time \( t = \frac{T}{2} \) are respectively:
- KEAM - 2024
- Physics
- speed and velocity
A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:
- JEE Main - 2024
- Physics
- speed and velocity
Questions Asked in JEE Main exam
- The area of the region enclosed by the curves \( y = x^2 - 4x + 4 \) and \( y^2 = 16 - 8x \) is:
- JEE Main - 2025
- Area between Two Curves
- Let $$ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. $$ Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$. If $a - A = 2$, and the ratio of the eccentricities of $E$ and $H$ is $\frac{1}{3}$, then the sum of the lengths of their latus rectums is equal to:
- JEE Main - 2025
- Conic sections
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
- JEE Main - 2025
- Matrix Algebra
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is $ 4 \_\_\_\_\_$.
- JEE Main - 2025
- permutations and combinations
Let \( f : (0, \infty) \to \mathbb{R} \) be a twice differentiable function. If for some \( a \neq 0 \), } \[ \int_0^a f(x) \, dx = f(a), \quad f(1) = 1, \quad f(16) = \frac{1}{8}, \quad \text{then } 16 - f^{-1}\left( \frac{1}{16} \right) \text{ is equal to:}\]
- JEE Main - 2025
- integral
Concepts Used:
Speed and Velocity
The rate at which an object covers a certain distance is commonly known as speed.
The rate at which an object changes position in a certain direction is called velocity.
Difference Between Speed and Velocity:
Read More: Difference Between Speed and Velocity