Final answer:
To find the weight of a mass on an unknown planet, we can use the formula Weight = mass x acceleration due to gravity. Given the length of the pendulum and the time for one complete oscillation, we can calculate the acceleration due to gravity on the unknown planet and then find the weight of a 5kg mass using the formula. The correct answer is d. 6.0 kg.
Step-by-step explanation:
To find the weight of a mass on an unknown planet, we need to use the formula:
Weight = mass x acceleration due to gravity
The acceleration due to gravity on the unknown planet can be calculated using the formula:
g = (4π²L) / T²
Where L is the length of the pendulum and T is the time taken for one complete oscillation.
Given that the pendulum has a length of 0.3m and does 20 complete oscillations in 39.6 seconds, we can substitute these values into the formula to get:
g = (4π² x 0.3) / (39.6/20)²
Solving this, we find g to be approximately 0.24 m/s².
To find the weight of a mass of 5kg on the unknown planet, we can now use the formula:
Weight = mass x acceleration due to gravity
Substituting in the values, we get:
Weight = 5 x 0.24 = 1.2 kg
Therefore, the correct option is d. 6.0 kg