A ball is dropped from height $H$ on to a horizontal surface. If the coefficient of restitution is $e$ then the total time after which it comes to rest is
- $\sqrt{\frac{2 H}{g}}\left(\frac{1 - \, e}{1 + \, e}\right)$
- $\sqrt{\frac{2 H}{g}}\left(\frac{1 + e}{1 - e}\right)$
- $\sqrt{\frac{2 H}{g}}\left(\frac{1 + e^{2}}{1 - \, e^{2}}\right)$
- $\sqrt{\frac{2 H}{g}}\left(\frac{1 - \, e^{2}}{1 + e^{2}}\right)$
The Correct Option is B
Solution and Explanation
Top Questions on Newtons Laws of Motion
Two blocks of masses \( m \) and \( M \), \( (M > m) \), are placed on a frictionless table as shown in figure. A massless spring with spring constant \( k \) is attached with the lower block. If the system is slightly displaced and released then \( \mu = \) coefficient of friction between the two blocks.
(A) The time period of small oscillation of the two blocks is \( T = 2\pi \sqrt{\dfrac{(m + M)}{k}} \)
(B) The acceleration of the blocks is \( a = \dfrac{kx}{M + m} \)
(\( x = \) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \( \dfrac{m\mu |x|}{M + m} \)
(D) The maximum amplitude of the upper block, if it does not slip, is \( \dfrac{\mu (M + m) g}{k} \)
(E) Maximum frictional force can be \( \mu (M + m) g \)Choose the correct answer from the options given below:
- JEE Main - 2025
- Physics
- Newtons Laws of Motion
- A block of mass \(2\, \text{kg}\) is placed on a smooth horizontal surface. A force of \(10\, \text{N}\) is applied horizontally on the block. What is the acceleration of the block?
- VITEEE - 2025
- Physics
- Newtons Laws of Motion
A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the coefficient of static friction between the block on the floor and the floor itself is
- KCET - 2025
- Physics
- Newtons Laws of Motion
- A force \( \mathbf{F} = ai + bj + ck \) is acting on a body of mass \( m \). The body was initially at rest at the origin. The co-ordinates of the body after time \( t \) will be:
- WBJEE - 2025
- Physics
- Newtons Laws of Motion
- A block of mass 2 kg is acted upon by a net force of 10 N. What is its acceleration?
- MHT CET - 2025
- Physics
- Newtons Laws of Motion
Questions Asked in NTA Abhyas exam
- Which of the following can show positive deviation from Raoult's law?
- NTA Abhyas - 2020
- Solutions
- A particle of mass $m$ and charge $q$ is thrown from a point in space where uniform gravitational field & electric field are present. The particle (1) may follow a straight line (2) may follow a circular path (3) may follow a parabolic path
- NTA Abhyas - 2020
- electrostatic potential and capacitance
- When two bodies collide elastically. The force of interaction between them is
- NTA Abhyas - 2020
- Elastic and inelastic collisions
- The dimensional formula for permittivity of free space $\left(\left(\epsilon \right)_{0}\right)$ in the equation $F=\frac{1}{4 \pi \epsilon _{0}}\frac{q_{1} q_{2}}{r^{2}}$ , where symbols have their usual meaning, is
- NTA Abhyas - 2020
- Dimensional Analysis
- The dimensional formula for entropy is
- NTA Abhyas - 2020
- Dimensional Analysis
Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.