A 60 kg block weighs 132 lb on Earth. If the block were transported to a planetary body that had a BIGGER free fall acceleration (as compared to Earth), which one of the following would be TRUE?
The block would have a smaller mass & a bigger weight.
The block would have a bigger mass & the same weight.
The block would have the same mass & a bigger weight.
The block would have a smaller mass & same weight.
My answer is no. 3.
To solve this question, we need to understand the relationship between weight, mass, and free fall acceleration. The weight of an object is the force with which it is attracted towards the center of the Earth (or any other planetary body). Weight is directly proportional to mass and the free fall acceleration.
On Earth, the free fall acceleration is approximately 9.8 meters per second squared (m/s^2). If the same block weighs 132 lb on Earth, we can find its mass by using the relationship:
Weight = mass × free fall acceleration
Re-arranging the equation to solve for mass:
mass = Weight / free fall acceleration
mass = 132 lb / 9.8 m/s^2
To compare the block's weight and mass on a planetary body with a bigger free fall acceleration, let's consider the options one by one:
1. The block would have a smaller mass & a bigger weight.
If the free fall acceleration is bigger, the mass would decrease according to the equation. However, the weight would actually increase because weight is directly proportional to both mass and free fall acceleration. Therefore, this statement is incorrect.
2. The block would have a bigger mass & the same weight.
Since the mass is directly proportional to the weight, if the mass increases, the weight would also increase. However, this statement suggests that the weight remains the same. Therefore, this statement is also incorrect.
3. The block would have the same mass & a bigger weight.
We have already established that if the free fall acceleration increases, the weight increases. However, this statement suggests that the mass remains the same. Therefore, this statement is incorrect.
4. The block would have a smaller mass & the same weight.
According to the equation mentioned earlier, if the free fall acceleration is bigger, the mass would decrease. If the mass decreases, the weight would also decrease because weight is directly proportional to mass. Therefore, this statement is correct.
So, the correct answer is: The block would have a smaller mass & the same weight.