in a physics laboratory a block x is balanced by a block Y of mass 200 kg,each are suspended from a balance of equal lever arms .the scale pan on X is at a height.div=2 cm ,where as scale pan on Y is at height 1 cm above the floor.the error in weighing is (in gram)

To determine the error in weighing between the two blocks, we need to consider the principle of moments and how the height of the scale pans affects the readings. Since both blocks are suspended from a balance with equal lever arms, the balance should ideally read equal weights if the system is perfectly calibrated. However, the difference in heights of the scale pans introduces a potential error in the weighing process.

Understanding the Setup

We have two blocks: Block X with an unknown mass and Block Y with a mass of 200 kg. The heights of the scale pans are as follows:

• Height of Block X's scale pan (H1) = 2 cm
• Height of Block Y's scale pan (H2) = 1 cm

Since both blocks are balanced, we can use the concept of torque, which is the product of the force (weight) and the distance from the pivot point (lever arm). In this case, the lever arms are equal, so we can focus on the weights and their respective heights.

Calculating the Effective Weight

The effective weight of each block can be influenced by the height of the scale pan. The weight can be thought of as being affected by the height at which it is measured. The formula for the effective weight (W_eff) can be simplified as:

W_eff = W × (1 - h/L)

Where:

• W = actual weight of the block
• h = height of the scale pan above the reference point (floor)
• L = total height of the balance system (which we can assume to be constant for both blocks)

Applying the Formula

For Block Y (200 kg), if we assume the total height L is the same for both blocks, we can express the effective weight of Block Y as:

W_eff(Y) = 200 kg × (1 - 1 cm/L)

For Block X, we have:

W_eff(X) = m × (1 - 2 cm/L)

Since the blocks are balanced, we can set these two effective weights equal to each other:

200 kg × (1 - 1 cm/L) = m × (1 - 2 cm/L)

Finding the Error

To find the mass of Block X (m), we can rearrange the equation. However, we also need to account for the difference in height when calculating the error in weighing. The difference in height between the two blocks is:

Δh = H1 - H2 = 2 cm - 1 cm = 1 cm

This height difference can lead to a discrepancy in the perceived weight. The error in weighing can be approximated by considering how much weight is effectively "lost" or "gained" due to this height difference.

Calculating the Error in Grams

Assuming a linear relationship, the error can be calculated as:

Error = (Δh / L) × 200 kg

To convert this into grams, we multiply by 1000 (since 1 kg = 1000 g):

Error = (1 cm / L) × 200,000 g

Without knowing the exact value of L, we cannot compute a numerical value for the error. However, if L were provided, you could substitute it into the equation to find the specific error in grams.

Summary

The error in weighing arises from the difference in height of the scale pans, which affects the effective weight readings of the blocks. By applying the principles of torque and effective weight, we can derive a formula to estimate this error, contingent on knowing the total height of the balance system. This illustrates how even small differences in height can lead to significant discrepancies in measurements in a physics laboratory setting.