Question

a straight rod of length extends from x=0 to x=L.The linear mass density of rod varies with x co-ordinate is lambda=a0+b0x^2.The gravitational force experienced by a point mass m at x=-a, is

where ^ means rest to

Answer 1

Answer on Question #65089-Physics-Mechanics-Relativity

A straight rod of length extends from $x = 0$ to $x = L$ . The linear mass density of rod varies with $x$ coordinate is $\lambda = a_0 + b_0x^2$ . The gravitational force experienced by a point mass $m$ at $x = -a$ , is

Solution

$$d F = \frac {G m \lambda d x}{x ^ {2}}$$

The gravitational force experienced by a point mass $m$ at $x = -a$ , is

$$F = \int_ {a} ^ {a + L} \frac {G m [ a _ {0} + b _ {0} x ^ {2} ] d x}{x ^ {2}} = a _ {0} \int_ {a} ^ {a + L} \frac {G m d x}{x ^ {2}} + b _ {0} \int_ {a} ^ {a + L} G m d x = G m \left[ a _ {0} \left(\frac {1}{a} - \frac {1}{a + L}\right) + b _ {0} L \right].$$

Answer: $Gm\left[a_0\left(\frac{1}{a} - \frac{1}{a + L}\right) + b_0L\right]$ .

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