Question

1.Three identical very dense masses of 3500 kg each are placed on the x axis. One mass is at x1 = -120 cm , one is at the origin, and one is at x2 = 300 cm .

What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses?

Take the gravitational constant to be G = 6.67×10⁻¹¹ N⋅m2/kg2 .

Express your answer in newtons to three significant figures.

2.Three identical very dense masses of 5000 kg each are placed on the x axis. One mass is at x1 = -100 cm , one is at the origin, and one is at x2 = 310 cm .

What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses?

Take the gravitational constant to be G = 6.67×10⁻¹¹ N⋅m2/kg2 .

Express your answer in newtons to three significant figures.

Answer 1

1.

Gravitational force is given by:

F = G*m1*m2/R^2

Net force on the mass at origin will be

Fnet = F2 - F1

m1 = m2 = m3 = m

Since gravitational force is always attractive force, So force due to mass at x1 will be towards -ve x-axis and force due to mass at x2 will be towards +ve x-axis.

Fnet = G*m*m/x1^2 - G*m*m/x2^2

Fnet = G*m^2*(1/x1^2 - 1/x2^2)

x1 = -120 cm = 1.20 m

x2 = 300 cm = 3.00 m

Using given values:

Fnet = 6.67*10^-11*3500^2*(1/3.00^2 - 1/1.20^2)

Fnet = -4.77*10^-4 N

Magnitude of F = |F| = 4.77*10^-4 N

(-ve sign means Net force will be towards -ve x-axis)

2.

Gravitational force is given by:

F = G*m1*m2/R^2

Net force on the mass at origin will be

Fnet = F2 - F1

m1 = m2 = m3 = m

Since gravitational force is always attractive force, So force due to mass at x1 will be towards -ve x-axis and force due to mass at x2 will be towards +ve x-axis.

Fnet = G*m*m/x1^2 - G*m*m/x2^2

Fnet = G*m^2*(1/x1^2 - 1/x2^2)

x1 = -100 cm = 1.00 m

x2 = 310 cm = 3.10 m

Using given values:

Fnet = 6.67*10^-11*5000^2*(1/3.10^2 - 1/1.00^2)

Fnet = -14.9*10^-4 N

Magnitude of F = |F| = 14.9*10^-4 N

(-ve sign means Net force will be towards -ve x-axis)

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