SSC 10th Science Maharashtra Board: Numerical Problem 3
Chapter 1 (Gravitation) - Question 5 (c)
Note: This is the 3rd numerical problem listed in the Gravitation chapter exercise.
The mass and weight of an object on earth are $5\text{ kg}$ and $49\text{ N}$ respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is $1/6$th of that on the earth.
Solution:
Given:
Mass of the object on earth ($m_e$) = $5\text{ kg}$
Weight of the object on earth ($W_e$) = $49\text{ N}$
Acceleration due to gravity on the moon ($g_m$) = $\frac{1}{6} g_e$ (where $g_e$ is the acceleration due to gravity on earth)To find:
Mass of the object on the moon ($m_m$) = ?
Weight of the object on the moon ($W_m$) = ?Calculation:
Step 1: Find the mass on the moon
Mass is a fundamental property of an object representing the amount of matter contained in it. It remains constant everywhere in the universe and does not change with location or gravitational force. Therefore, the mass of the object on the moon will be the same as its mass on the earth.$$m_m = m_e = 5\text{ kg}$$
Step 2: Find the weight on the moon
Weight is the gravitational force acting on an object, given by the formula $W = mg$.
The weight of the object on the moon will depend on the acceleration due to gravity on the moon.$$W_m = m \times g_m$$
Substitute the given condition $g_m = \frac{1}{6} g_e$:
$$W_m = m \times \left(\frac{1}{6} g_e\right)$$
$$W_m = \frac{1}{6} \times (m \times g_e)$$
Since the weight on earth is $W_e = m \times g_e$, we can substitute $W_e$:
$$W_m = \frac{1}{6} \times W_e$$
$$W_m = \frac{1}{6} \times 49$$
$$W_m = 8.167\text{ N}$$
Answer:
The mass of the object on the moon will be $5\text{ kg}$ and its weight will be approximately $8.17\text{ N}$.
