Question:
Water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. The height, in m, of the second drop above the ground at that instant is (Take g = 10 m s$^{-2}$)
Water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. The height, in m, of the second drop above the ground at that instant is (Take g = 10 m s$^{-2}$)
Updated On: May 12, 2024
- 1.25
- 2.5
- 3.75
- 5
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Given, height of tap from ground,$h=.5m$
$g= 10\, m \,s^{-2}$
Time taken by first drop to reach the ground,
$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2\times5}{10}} = \sqrt{1} =1 s$
Now, if first drop falls at O s, and second drops at 1/2 s, then third drop will fall at 1 s as they fall on equal time interval.
At $t = 1\, s$, distance covered by 2$^{nd}$ drop is,
$h' =\frac{1}{2} gt^{'2} = \frac{1}{2}\left(10\right)\left(\frac{1}{2}\right)^{2} = \frac{10}{8} = 1.25 m$
Height of the second drop from the ground,
= $h- h'$
= 5 -1.25 = 3.75 m.
$g= 10\, m \,s^{-2}$
Time taken by first drop to reach the ground,
$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2\times5}{10}} = \sqrt{1} =1 s$
Now, if first drop falls at O s, and second drops at 1/2 s, then third drop will fall at 1 s as they fall on equal time interval.
At $t = 1\, s$, distance covered by 2$^{nd}$ drop is,
$h' =\frac{1}{2} gt^{'2} = \frac{1}{2}\left(10\right)\left(\frac{1}{2}\right)^{2} = \frac{10}{8} = 1.25 m$
Height of the second drop from the ground,
= $h- h'$
= 5 -1.25 = 3.75 m.
Was this answer helpful?
0
0
Top Questions on Motion in a straight line
- A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _______m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- The displacement and the increase in the velocity of a moving particle in the time interval of \( t \) to \( (t + 1) \) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in \( (t + 2)^{\text{th}} \) s is \( \_\_\_\_ \) m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- Two cars are travelling towards each other at a speed of \( 20 \, \text{m/s} \) each. When the cars are \( 300 \, \text{m} \) apart, both the drivers apply brakes and the cars retard at the rate of \( 2 \, \text{m/s}^2 \). The distance between them when they come to rest is:
- JEE Main - 2024
- Physics
- Motion in a straight line
- A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\ ms^{-1}\). The ball strikes the water surface after \(4s\). The height of bridge above water surface is
(Take: \(g=10\ ms^{-2}\))- NEET (UG) - 2023
- Physics
- Motion in a straight line
- A bullet from a gun is fired on a rectangular wooden block with velocity u. When the bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
- NEET (UG) - 2023
- Physics
- Motion in a straight line
View More Questions
Questions Asked in COMEDK UGET exam
- A $2\,kg$ mass lying on a table is displaced in the horizontal direction through $50\,cm$. The work done by the normal reaction will be
- COMEDK UGET - 2015
- work, energy and power
- The numbers of $ {H^+}$ ions present in 1 mL of a solution whose pH is 13
- COMEDK UGET - 2015
- Equilibrium
- A mixture of methylamine and dimethylamine is given to you. The reagents used to separate the components of the mixture are
- $\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$
- COMEDK UGET - 2015
- Inverse Trigonometric Functions
- Pick the incorrect statement among those given below.
- COMEDK UGET - 2015
- Chemical bonding and molecular structure
View More Questions
Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.