Three different objects of masses m₁, m₂ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$m_{1} : 2 m_{2} : 3 m_{3}$

$m_{1} : m_{2} : m_{3}$

1 : 1 : 1

$\frac{1}{m_{1}} : \frac{1}{m_{2}} : \frac{1}{m_{3}}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Velocity is independent of mass

When objects fall freely under gravity along different frictionless paths, their velocities and accelerations may vary, but the displacements they cover in equal time intervals will be equal. This is because the only force acting on the objects is gravity, and the gravitational force acts vertically downward. As a result, the objects will have the same vertical displacements in equal time intervals.

Let's assume the objects fall for a certain time interval Δt. During this time, each object will experience the same acceleration due to gravity, g. Therefore, the vertical displacement of each object can be calculated using the equation:

$d = \frac{1}{2} g Δ t^{2}$

Since g and $Δ t^{2}$ are constant for all objects, the displacements will be proportional to each other. Thus, the displacements in equal time intervals will be equal.

Therefore, option C is the correct choice: Displacements in equal time intervals are equal.

Watch 3-min video & get full concept clarity