Question

10) 1. A 50 kg object is placed between a 400 kg and a 900 kg objects which are separated by a distance of 2 m. (a) What is the net gravitational force exerted on 50 kg object by the other two? (b) At what position the 50 kg object be placed so the net force on it will be zero? (10 2. Compare the gravitational forces between the moon and the earth and the moon and the sun if the mass of the moon is 7.36x1022 kg, the mass of the earth is 5.98x1024 kg and the mass of the sun is 1.99x1030 kg. The average distance of the moon from the earth is 3.84x108 m and from the sun is 1.492x1011 m. 3. Two blocks of masses 5 kg and 9 kg are connected by a uniform string of negligible mass and length I as shown in the Fig. 1. One block is placed on a smooth horizontal plane and the other hangs over the side. Describe the motion of the system using Lagrange's equation and find the acceleration of the system. (20- 4. A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other, as shown in Fig. 2. If both pendula have equal lengths and have bobs of equal mass and both are moving in the same plane, find the Lagrange's equations of motion for the system. ( for bolti o, e o

Answer 1

the gravitationed for ce on due to my in G mm, F = 6 mm - 2 ۷ (۲) الا m.is Similarly, force - Gimme on m due to - 4 G mome so the net foro on mn F=Fitry – 4 Gum, 290 m F = 46m (mama) Given. ma- 50kg, ma- 400kg, me gookg. 2 6.6 TXIO" SI duit. &-2m. 6. 67x10x50 (kinn. = 900 & 900) 2 6.67 x loxox130 F = 1.08x10 6N

Gravitational force between roon & Earth F G Mm MG 2 Ms Mm . for a between Similarly Moon & Sun is G Mm MG Taking radio; & Geheime vie Fr X GYM - Mc " sa 3.84X Lom, r = 1.492810 m, ME=H. 98 x 104 kg Ms = 1.99 x 10 kg B 1.4 22x100 g 5.988124 3.84x108) 1.99xlo » 30 ) = 0.45 » Fi= 0.45X F2 Fosce between moon & Enth 04sx (fron between o noon & sem)

maferin) 4. hom diagram 7 = Conor Y = l, core, & lords and a a d sind ar & könor & lsina we can find that | - - K , Sinh 7 ) - - 1 o, sied) - 2 oz sinda and a los lore). xal, 0, lord, & & & coro- Kinetic beaty of the system, Tam, (2) ty, ) & traz (A2+2) - tm 8 or + me lion de + 21, le concorded] The potential wegen of the system, va un gl hli- bieloro,] meghirden (cao, to then Lagrang; an, = Tv o m 8,967 timp in the pat 24,,40,491,60,7 - Ek+1, -, 6011 - 3[4,424 (6, 40, 4 12 (2) Laceton2]

pulting 2 l = l od mamam. Then, L = 4 m pret + f n (t + 1 2 + 2 tre cos (9-0)] -mg124-86006) - mg (24-16374 cm)] - in front mere intojo cos (or B2) - 4 mg 1 + 2 mgl cord & mgf corde. Sorry I am not able to do answer