A rod of length L with non-uniform mass distribution is hinged horizontally to a vertical wall...

 

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A rod of length L with non-uniform mass distribution is hinged horizontally to a vertical wall from one end. The rod is supported by a rope from the other end as shown in the figure such that the rope makes an angle of 30 with the horizontal. The linear mass density (mass per unit of length) of the rod is X(x)=8Cx/L4 where x is the distance from the hinge (x L) and C is a constant. The unit of C is kg. The distance between point mass m and the hinge is L/2. . What is mass M of the rode? (a) 8C/3 (b) 2C (c) C/2 (d) C (e) 2C/3 . Find distance LG between the hinge and the centre of gravity of the rode (do not take into account point mass m). (e) 3L/4 (a) 2L/3 (b) L/5 (c) L/3 (d) 4L/5 L/2 m . Find the tension in the rope (as mass m is much smaller than the mass of the rode M neglect mass m) (a) gMLG/Ltan(30) (b) gMLG/Lcos (30) (c) gMLGsin (30)/L (d) gMLG/Lsin (30) (e) gML/Lcsin (30) 8 M A rod of length L with non-uniform mass distribution is hinged horizontally to a vertical wall from one end. The rod is supported by a rope from the other end as shown in the figure such that the rope makes an angle of 30 with the horizontal. The linear mass density (mass per unit of length) of the rod is X(x)=8Cx/L4 where x is the distance from the hinge (x L) and C is a constant. The unit of C is kg. The distance between point mass m and the hinge is L/2. . What is mass M of the rode? (a) 8C/3 (b) 2C (c) C/2 (d) C (e) 2C/3 . Find distance LG between the hinge and the centre of gravity of the rode (do not take into account point mass m). (e) 3L/4 (a) 2L/3 (b) L/5 (c) L/3 (d) 4L/5 L/2 m . Find the tension in the rope (as mass m is much smaller than the mass of the rode M neglect mass m) (a) gMLG/Ltan(30) (b) gMLG/Lcos (30) (c) gMLGsin (30)/L (d) gMLG/Lsin (30) (e) gML/Lcsin (30) 8 M

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Lets solve each part of this question step by step Part 1 What is the mass M of the rod Mass M is the integral of the linear density over the length o... View the full answer