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A 20 N metal block is suspended by a spr...

A `20 N` metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads `40 N`. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads `16 N`. The reading of the weighing machine will be.

A

36 N

B

60 N

C

44 N

D

56 N

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will analyze the forces acting on the metal block and the beaker containing water. ### Step 1: Identify the forces acting on the block The metal block has a weight of 20 N acting downwards. When it is immersed in water, it experiences a buoyant force acting upwards. The spring balance reads 16 N when the block is fully immersed. ### Step 2: Calculate the buoyant force The buoyant force can be calculated using the difference between the weight of the block and the reading of the spring balance when the block is immersed. \[ \text{Buoyant Force} = \text{Weight of the Block} - \text{Reading of the Spring Balance} \] \[ \text{Buoyant Force} = 20 \, \text{N} - 16 \, \text{N} = 4 \, \text{N} \] ### Step 3: Analyze the forces acting on the beaker The beaker has a weight of 40 N, and when the block is immersed, it experiences an additional downward force due to the buoyant force acting on it. According to Newton's third law, the buoyant force exerted by the water on the block is equal and opposite to the force exerted by the block on the water. ### Step 4: Calculate the total force acting on the weighing machine The normal force (reading of the weighing machine) is the sum of the weight of the beaker and the buoyant force acting on it: \[ \text{Normal Force} = \text{Weight of the Beaker} + \text{Buoyant Force} \] \[ \text{Normal Force} = 40 \, \text{N} + 4 \, \text{N} = 44 \, \text{N} \] ### Step 5: Conclusion The reading of the weighing machine will be 44 N. ### Summary of the Solution 1. Weight of the block = 20 N 2. Reading of the spring balance when immersed = 16 N 3. Buoyant force = 20 N - 16 N = 4 N 4. Weight of the beaker = 40 N 5. Reading of the weighing machine = 40 N + 4 N = 44 N ### Final Answer The reading of the weighing machine will be **44 N**. ---
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