1.

Which of the following statements are true ? (i) A uniform wooden plank of mass 150 kg and length 8 m is floating on still water with a man of 50 kg at one end of it. The man walks to the other end of the plank and stops. The distance covered by the plank is 2 m. (ii) A kid of mass 15 kg is sitting in a boat of mass 45 kg in a lake. The distance of kid from the bank of lake is 12 m. Now the body moves inside the boat at a distance 4m towards the bank and stops. The distance of the kid from the bank (there is no friction between the water and the boat ) is 11 m. (iii) Two persons of masses 40 kg and 60 kg are sitting at the midpoint of a 12 -m- long boat (140 kg) standing still in water. Now they move to opposite ends of the boat. Neglecting the friction between boat and water, the distance traveled by the boat in water is 50 cm. (iv) In a gravity free space , a man of mass m standing at a height h above the floor, throws a ball of mass m_(0) straight down with a speed v_(0). When the ball reaches the floor, the distance of the man above the floor is (1 + (m_(0))/(m))h.

Answer»

`(i),(ii)`
(i) ,(III) ,(iv)`
`(ii) ,(iii) ,(iv)`
all of the above

Solution :In the following CASES , `vec(F)_(ext) = 0` , the system is initially at rest and hence the location of center of mass is fixed.
(i) Let the distance covered by the PLANK is `d`.
`m_(1) x_(1) = m_(2) x_(2)`
`50 (8 - d) = 150 d rArr d = 2m`
`(i) is O.K.`
(ii) Let the distance travelled by boat is `d`.
`15(4 - d) = 45 d rArr d = 1m`
Distance of boy from the bank of the river is
`(12 - 4) + d = 8 + 1 = 9 m`
`(ii)` is incorrect.
(iii) Let the distance travelled by the boat be `d`.
`60(6 -d) = 40( 6 + d) + 140 d`
`rArr d = (1)/(2) m = 50 CM`
`(iii) is O.K`.
(iv) `m_(0) h = mh' rArr h' = (m_(0))/(m) h`
Distance of man above the floor is
`h + h' = (1 + (m_(0))/(m))h`
`(iv) is O.K`.


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