Problem 61 - A Complete Resource Book in Physics for JEE Main

Question

A pebble of mass \(0.05 \mathrm{~kg}\) is thrown vertically upwards. The direction and magnitude of the net force on the pebble is given below, choose the incorrect option. (A) During its upward motion, force is \(0.5 \mathrm{~N}\) in vertically upward. (B) During its downward motion, force is \(0.5 \mathrm{~N}\) in vertically downward. (C) At the highest point, where it is momentarily at rest, force is \(0.5 \mathrm{~N}\) in vertically downward. (D) If the pebble was thrown at an angle of say \(45^{\circ}\) with the horizontal direction, force is \(0.5 \mathrm{~N}\) in vertically downward (Ignoring air resistance).

Step-by-Step Solution

Answer

The incorrect option is (A) During its upward motion, force is $0.5 \mathrm{~N}$ in vertically upward. The actual gravitational force acting on the pebble in the opposite direction is $0.4905\,\text{N}$.

Step 1: Calculate the weight of the pebble

The weight (gravitational force) acting upon the pebble can be determined using the formula \(W = m \cdot g\), where 'm' represents the mass, and 'g' is the acceleration due to gravity, approximated as \(9.81\,\text{m/s}^2\). \[W = 0.05\,\text{kg}\times 9.81\frac{\text{m}}{\text{s}^2} = 0.4905\,\text{N}\] 2. Evaluate each option based on the principles of Newton's laws of motion and the gravitational force calculated.

Step 2: Evaluate the options

(A) During the pebble's upward motion, the gravitational force (weight) pulls it vertically downward with a force of \(0.4905\,\text{N}\). The fact that it is experiencing a force of \(0.5\,\text{N}\) vertically upward is incorrect, since it would need a force equal and opposite to the gravitational force, which would be \(0.4905\,\text{N}\). (B) When the pebble is in its downward motion, indeed it is acted upon by a gravitational force of \(0.4905\,\text{N}\), which is very close to \(0.5\,\text{N}\) vertically downward. This is a correct option. (C) At the highest point, where the pebble is momentarily at rest, the force acting on it is still the gravitational force, which is \(0.4905\,\text{N}\). So, the statement claiming the force is \(0.5\,\text{N}\) is also close to the real value, and it's vertically downward. This statement is also correct. (D) If the pebble is thrown at any angle (ignoring air resistance), the force acting on the pebble still must be the gravitational force, acting vertically downward. This option appears to be also correct, considering the value is a close approximation to the real gravitational force acting on the pebble. In summary, statement (A) is the only incorrect option based on the analysis of gravitational force acting on the pebble and the understanding of Newton's laws of motion principles.