A mass m is at a distance a from one end of a uniform rod of length l and mass M. Find the gravitational force on the mass due to the rod.
Text Solution
Verified by Experts
As m is a point mass, consider an element on the rod at distance `r` from `m` `dF=(G(m)(dm))/(r^(2))=(G(m)(M/L)dr)/(r^(2))` or `F=int_(d)^(L+d)(Gmm)/L 1/(r^(2))dr =(GMm)/L int_(d)^(L+d) 1/(r^(2)) dr=(GMm)/(d(L+d))`
Topper's Solved these Questions
GRAVITATION
CENGAGE PHYSICS|Exercise Exercise 6.1|13 Videos
GRAVITATION
CENGAGE PHYSICS|Exercise Exercise 6.2|15 Videos
FLUID MECHANICS
CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos
KINEMATICS-1
CENGAGE PHYSICS|Exercise Integer|9 Videos
Similar Questions
Explore conceptually related problems
A mass m is at a distance a from one end of a uniform rod of length l and mass M. Find the gravitational force on the mass due to tke rod.
A point mass body of mass 2 kg is placed at a distance 20 cm from one end of a uniform rod of length 2 m and mass 10 kg . Calculate (i) gravitational intensity at the location of point mass body due to the rod. (ii) gravitational force on the body due to the rod. Use G = 6.67 xx 10^(-11) Nm^(2) kg^(-2) .
A particle of mass m is situated at a distance d from one end of a rod of mass M and length L as shown in diagram. Find the magnitude of the gravitational force between them
Two uniform solid of masses m_(1) and m_(2) and radii r_(1) and r_(2) respectively, are connected at the ends of a uniform rod of length l and mass m . Find the moment of inertia of the system about an axis perpendicular to the rod and passing through a point at a distance of a from the centre of mass of the rod as shown in figure.
A uniform thin rod of length 3 L is bent at right angles at a distance L from one end as shown in Fig. If length of rod is 1.8m , find the co-ordinates and position vector of the mass of the system.
(a) A uniform rod of mass M and length L is placed at distance L from a point mass m as shown. Find force on m (b) A semiconductor wire has a length L and mass M . A particle of mass m is placed at the centre of the circle. find the gravitational attraction on the particle due to the wire.
Show that the centre of mass of uniform rod of mass M and length L lies at the middle point of the rod.
