Advertisements
Advertisements
प्रश्न
It is a common observation that rain clouds can be at about a kilometre altitude above the ground.
- If a rain drop falls from such a height freely under gravity, what will be its speed? Also calculate in km/h. ( g = 10 m/s2)
- A typical rain drop is about 4mm diameter. Momentum is mass x speed in magnitude. Estimate its momentum when it hits ground.
- Estimate the time required to flatten the drop.
- Rate of change of momentum is force. Estimate how much force such a drop would exert on you.
- Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5 cm.
(Assume that umbrella is circular and has a diameter of 1 m and cloth is not pierced through !!)
Advertisements
उत्तर
Given, height (h) = 1 km = 100 m
g = 10 m/s2
a. Velocity attained by the raindrop in freely falling through a height h.
v = `sqrt(2gh)`
= `sqrt(2 xx 10 xx 1000)`
= `100sqrt(2)` m/s
= `100sqrt(2) xx (60 xx 60)/1000` km/h
= `360sqrt(2)` km/h ≈ 510 km/h
b. Diameter of the drop (d) = 2r = 4 mm
∴ Radius of the drop (r) = 2 mm = 2 × 10–3 m
Mass of a raindrop (m) = V × p
= `4/3 pir^3p`
= `4/3 xx 22/7 xx (2 xx 10^-3)^3 xx 10^3` .....(∵ Density of water = 103 kg/m3)
= 3.4 × 10–5 kg
The momentum of the raindrop (p) = mv
= `3.4 xx 10^-5 xx 100sqrt(2)`
= `4.7 xx 10^-3` kg-m/s
≈ `5 xx 10^-3` kg-m/s
c. Time required to fatten the drop = time taken by the drop to travel the distance equal to the diameter of the drop near the ground
`t = d/v`
= `(4 xx 10^3)/(100 sqrt(2))`
= ``0.028 xx 10^-3` s
= `2.8 xx 10^-5` s ≈ 30 ms
d. Force exerted by a raindrop
F = `"Change in momentum"/"Time"`
= `(p - 0)/t`
= `(4.7 xx 10^-3)/(2.8 xx 10^-5)` ≈ 168 N
e. Radius of the umbrella (R) = `1/2` m
∴ Area of the umbrella (A) = `piR^2`
= `22/7 xx (1/2)^2`
= `22/28`
= `11/4 ≈ 0.8` m2
Number of drops striking the umbrella simultaneously with an average separation of 5 cm = `5 xx 10^-2` m
= `0.8/(5 xx 10^-2)^2` = 320
∴ Net force exerted on umbrella = 320 × 168 = 53760 N ≈ 54000 N.
APPEARS IN
संबंधित प्रश्न
At which point on its path a projectile has the smallest speed?
A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.
A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find the average velocity during this period .
A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
A ball is projected vertically upward with a speed of 50 m/s. Find the maximum height.
A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take in reaching the ground?
An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is 6 ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator.
A ball is thrown horizontally from a point 100 m above the ground with a speed of 20 m/s. Find the horizontal distance it travels before reaching the ground .
A ball is thrown at a speed of 40 m/s at an angle of 60° with the horizontal. Find the maximum height reached .
A ball is thrown at a speed of 40 m/s at an angle of 60° with the horizontal. Find the range of the ball. Take g = 10 m/s2.
In a soccer practice session the football is kept at the centre of the filed 40 yards from the 10 ft high goalposts. A goal is attempted by kicking the football at a speed of 64 ft/s at an angle of 45° to the horizontal. Will the ball reach the goal post?
A ball is projected from a point on the floor with a speed of 15 m/s at an angle of 60° with the horizontal. Will it hit a vertical wall 5 m away from the point of projection and perpendicular to the plane of projection without hitting the floor? Will the answer differ if the wall is 22 m away?
A bomb is dropped from a plane flying horizontally with uniform speed. Show that the bomb will explode vertically below the plane. Is the statement true if the plane flies with uniform speed but not horizontally?
A person is standing on a truck moving with a constant velocity of 14.7 m/s on a horizontal road. The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8 m. Find the speed and the angle of projection as seen from the road.
A man is sitting on the shore of a river. He is in the line of 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.
A river 400 m wide is flowing at a rate of 2.0 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water, in a direction perpendicular to the river. Find the time taken by the boat to reach the opposite bank.
A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river.
