A body of mass kg suspended at the 15cm mark of a ruler balanced if at the 30cm mark on a pivot.if the ruler has a mass of 36g and it entime a gravity is at 55cm mark.culate (I)mass (ii) distance of the balance point of the ruler from the 3 and when the body is removed to the 25cm mark.
To solve this problem, let's break it down step by step:
Step 1: Define the variables
Let's assign variables to the unknowns:
- Mass of the body: m (in kg)
- Distance of the balance point of the ruler from the pivot: d (in cm)
Step 2: Calculate the mass of the ruler
The ruler has a given mass of 36g, which we need to convert to kg:
mass_of_ruler = 36g = 0.036kg
Step 3: Calculate the total torque on the ruler
When the system is in equilibrium, the sum of the torques on the ruler must be zero. The torque (τ) is given by the formula τ = force x distance.
The torque due to the ruler itself is:
torque_ruler = mass_of_ruler x gravity x distance_of_ruler_from_pivot
torque_ruler = 0.036kg x 9.8m/s^2 x 55cm = 0.036kg x 9.8m/s^2 x 0.55m
Step 4: Calculate the torque due to the body
The torque due to the body suspended at the 15cm mark is:
torque_body = m x 9.8m/s^2 x 15cm = m x 9.8m/s^2 x 0.15m
Step 5: Set up the torque equation
Since the system is in equilibrium, the sum of the torques must be zero:
torque_ruler + torque_body = 0
Step 6: Solve for mass (m)
Substitute the values into the torque equation and solve for the mass (m):
0.036kg x 9.8m/s^2 x 0.55m + m x 9.8m/s^2 x 0.15m = 0
Simplify the equation and solve for m.
Step 7: Calculate the distance (d) when the body is at the 25cm mark
Since the system is still in equilibrium, we can use the same torque equation. However, the distance of the body from the pivot changes to 25cm.
Repeat step 3 and substitute the values to calculate the new torque of the ruler. Then solve the torque equation for the new distance (d).
Note: Remember to convert centimeters to meters in the calculations.
By following these steps, you should be able to solve the problem and determine the mass of the body (m) and the distance of the balance point of the ruler from the pivot (d).