Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is
\(\frac 54\)
\(\frac 85\)
\(\frac 58\)
\(\frac 45\)
The Correct Option is D
Solution and Explanation
We know from equation of motion that when a body is dropped
\(t =\sqrt {\frac {2h}{g}}\)
\(\frac {t_A }{ t_B }= \frac {(\sqrt {\frac {2h_A}{g}})}{(\sqrt {\frac {2h_B}{g}})}\)
\(\frac {h_A}{h_B }= \sqrt {\frac {16}{25 }}\)
\(\frac {h_A}{h_B }\) \(=\frac 45\)
So, the correct option is (D): \(\frac 45\)
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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.