A person standing on the floor of a lift drops a coin. The...

A person standing on the floor of a lift drops a coin. The coin reaches the floor of the lift in time if the lift is stationary and the time $\mathrm{t}_{2}$ if it is accelerated in upward direction. Than (A) $t_{1}=t_{2}$ (B) $\mathrm{t}_{1}>\mathrm{t}_{2}$ (C) $t_{1}<t_{2}$ (D) Cannot say anything

A person standing on the floor of a lift drops a coin. The coin reaches the floor of the lift in time if the lift is stationary and the time $\mathrm{t}_{2}$ if it is accelerated in upward direction. Than
(A) $t_{1}=t_{2}$
(B) $\mathrm{t}_{1}>\mathrm{t}_{2}$
(C) $t_{1}<t_{2}$
(D) Cannot say anything

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Key Concepts

Kinematics of Free Fall

The kinematics of free fall describe the motion of objects under the influence of constant acceleration, typically gravity. When the effective acceleration increases due to additional upward acceleration of the lift, the same distance is covered in a shorter time, according to the equation d = 1/2 * a_eff * t². This means that the time taken for the coin to reach the floor is less in an upward accelerating lift than when it is stationary.

Effective Gravity

Effective gravity refers to the net acceleration acting on objects in a non-inertial reference frame, which is the vector sum of real gravitational acceleration and any additional acceleration of the frame. In the context of an upward accelerating lift, the effective gravitational acceleration experienced by the coin increases to (g + a), which causes the coin to fall more quickly relative to the accelerating frame.

Non-Inertial Frames

A non-inertial frame is a reference frame that is accelerating relative to an inertial frame. In such frames, fictitious forces appear to act on objects, affecting their motion. In the case of an accelerated lift, observers inside the lift experience an increase in apparent gravitational pull, altering the coin's free-fall dynamics compared to when the lift is stationary.

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