a) consider an element of length dz and mass dm at a distance of z from mass m on the rod. Force due to this element will be Gmdm/z2. dm = Mdz/L.
Now for total mass integrate it from x = z to x = z+L.
F = GMm/z(z+L). Towards - z direction.
b). Consider an element of length dz at a distance of z from the upper end of lower rod having mass dm.
F on that dm will be GMdm/z(z+L).
DM will be again Mdz/L.
Now integrate it from z= L to z= 2L.
Consider a thin uniform rod of mass M and length L, positioned along the z-axis with...
A uniform thin rod of mass M and length L lies on the positive x-axis with one end at the origin.Consider an element of the rod of length dx., and mass dm at point where 0<x<L. a) What is the gravitational field produced by the mass element of any value of X? b)Calculate the total gravitational field produced by the rod. C)Find the gravitational force on a point particle of mass m0 at x0. D) Show that for x0>>L the...
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A long thin rod of length L = 8m and mass 5.5 kg with a uniform mass density is laid parallel to the x-axis and is rotated about a y-axis at L = 3m. Calculate its Moment of Inertia
(a) Knowing that the moment of inertia of a thin uniform metallic rod of mass m and length L about an axis through its center of mass is (1/12) ml?, what is its moment of inertial about a parallel axis through one of its ends (show your calculation). (b) A physical pendulum consisting of a thin metallic rod of mass m = 200.0 g and of length L = 1.000 m is suspended from the upper end by a frictionless...
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20. A thin rod of mass M and length L gravitationally interacts with a point mass m that is a perpendicular distance a away from its left end (see the figure). The rod is non-uniform, and its linear density (mass per unit length) increases with the distance from its left end according to 2(x) = 2Mx/L?, where x is the horizontal coordinate along the rod (so that x = 0 is at its left end and x=L is at its...
(a) Knowing that the moment of inertia of a thin uniform metallic rod of mass m and length L about an axis through its center of mass is (1/12) mL?. what is its moment of inertial about a parallel axis through one of its ends (show your calculation). (b) A physical pendulum consisting of a thin metallic rod of mass m = 200.0 g and of length L - 1.000 m is suspended from the upper end by a frictionless...
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