A hydraulic crane supports a mass of 500 kg with its piston cylinder actuator 60 cm, inclined at 60° with horizontal, as shown in figure. The diameter of the piston is 30 cm, acceleration due to gravity is 10 m/s². Neglecting mass of the piston, the reading of the pressure in kPa (gauge).

The correct option is 61.26.

Based on the provided diagram, we can identify the following parameters and details:
- A reservoir containing Oil with a Pressure gauge mounted on top.
- A piston-cylinder actuator inclined at an angle of 60° relative to the horizontal.
- A load of 500 kg supported by the piston shaft.

To find the gauge pressure reading, we carry out the calculations in the following steps:

Step 1: Calculate the weight of the supported mass
The downward force exerted by the mass due to gravity is the weight ($W$):

$$W=m·g$$

Given parameters:
- Mass, $m=500\text{kg}$
- Acceleration due to gravity, $g=10{\text{m/s}}^2$

Substituting these values:

$$W=500\text{kg}·10{\text{m/s}}^2=5000\text{N}$$

Step 2: Determine the force component acting along the axis of the actuator
Since the cylinder is inclined at 60° with the horizontal, the axial force ($F$) acting along the piston axis to support the vertical load is:

$$F=W·sin(60°)$$

Substituting the weight value:

$$F=5000\text{N}·sin(60°)=5000·0.866025\approx 4330.13\text{N}$$

Step 3: Calculate the cross-sectional area of the piston
The diameter of the piston is given as 30 cm, which is 0.3 m. The cross-sectional area ($A$) is calculated as:

$$A=\frac{\pi }{4}·d^2$$

Substituting $d=0.3\text{m}$:

$$A=\frac{\pi }{4}·{\left(0.3\right)}^2=\frac{\pi }{4}·0.09\approx 0.070686{\text{m}}^2$$

Step 4: Calculate the gauge pressure
The pressure ($P$) exerted on the oil by the piston is the axial force divided by the area of the piston:

$$P=\frac{F}{A}$$

Substituting the values of $F$ and $A$:

$$P=\frac{4330.13}{0.070686}\approx 61258.7\text{Pa}$$

Converting the pressure to kPa:

$$P=\frac{61258.7}{1000}\approx 61.26\text{kPa}$$

Therefore, the reading of the pressure gauge is 61.26 kPa (gauge).