A piston of cross sectional area 100cm2 is used in hydraulic to exert a force of 10000000dyne find the cross area of another having weight 2000kg

a

To find the cross-sectional area of the second piston, we can use the concept of hydraulic pressure. The pressure exerted by a given force on a piston is directly proportional to the force applied and inversely proportional to the cross-sectional area of the piston.

We are given the following information:
- Force exerted by the first piston: 10,000,000 dyne
- Cross-sectional area of the first piston: 100 cm²

First, we need to convert the force from dyne to newtons since the standard unit for force is Newton (N). The conversion factor is 1 dyne = 0.00001 N. Therefore, the force exerted by the first piston in Newtons is:
10,000,000 dyne * 0.00001 N/dyne = 100 N

Next, we can use the principle of Pascal's law to find the cross-sectional area of the second piston. According to Pascal's law, the pressure applied to a fluid in an enclosed space is transmitted undiminished to all portions of the fluid and to the walls of its container.

So, using the formula for hydraulic pressure, which is:
Pressure = Force / Area

We can rearrange the formula to solve for the cross-sectional area of the second piston:
Area = Force / Pressure

The weight of an object can be calculated using the formula:
Weight = Mass * Gravitational acceleration
where the gravitational acceleration is approximately 9.8 m/s².

Therefore, we have:
Weight = 2000 kg * 9.8 m/s² = 19,600 N

Now, we can find the cross-sectional area of the second piston:
Area = Force / Pressure = 19,600 N / 100 N/cm²

However, we need to make a unit conversion to match the units in the problem. Since the gravitational unit is given in kg and the cross-sectional area is given in cm², we need to convert the area unit from m² to cm². Since 1 m² = 10,000 cm², we can proceed with the conversion as follows:

Area = 19,600 N / 100 N/cm²
= 196 cm²

Therefore, the cross-sectional area of the second piston is 196 cm².