A body floats in a liquid contained in a beaker. The whole system as shown in Figure falls freely under gravity. The upthrust on the body is/are

Step 1: Identify the system state and effective gravity.

In a freely falling frame of reference, the downward acceleration of the beaker and liquid is $a = g$. The effective acceleration due to gravity $g_{\text{eff}}$ inside the system is:

$$g_{\text{eff}} = g - a$$ $$g_{\text{eff}} = g - g = 0$$

Step 2: Analyze the pressure gradient in the liquid.

The variation of pressure $p$ with depth $h$ in a liquid depends on the effective gravity.

$$\frac{dp}{dh} = \rho g_{\text{eff}}$$

Since $g_{\text{eff}} = 0$:

$$\frac{dp}{dh} = 0$$

This means there is no pressure difference between any two points in the liquid during free fall.

Step 3: Calculate the upthrust (buoyant force) on the body.

The upthrust $F_B$ arises due to the pressure difference in the liquid, which is given by:

$$F_B = \rho V_{\text{sub}} g_{\text{eff}}$$

Substituting $g_{\text{eff}} = 0$:

$$F_B = 0$$

Step 4: Evaluate the options.

The actual weight of the displaced liquid ($\rho V_{\text{sub}} g$), the weight of the body in air ($mg$), and the weight of the immersed portion of the body are all non-zero. Since the upthrust is exactly zero, the other options are incorrect.

Answer: The upthrust on the body is zero (Option 1).