Advertisements
Advertisements
प्रश्न
An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?
Advertisements
उत्तर १
Here v = 720 km/h = `720xx 5/18` m/s = 200 m/s and angle of banking `theta = 15^@`
From the relation
`tan theta = v^2/"rg"` we have
`r = v^2/(g tan theta) = (200xx200) /(10 xx tan 15^@) = (200xx200)/(10xx0.2679)`
=> r = 14931 m = 14.9 km
उत्तर २
Speed of the aircraft, v = 720 km/h = `720xx5/18 = 200` m/s
Acceleration due to gravity, g = 10 m/s2
Angle of banking, θ = 15°
For radius r, of the loop, we have the relation:
`tan theta = v^2/"rg"`
`r = v^2/(g tan theta)`
`= (200xx200)/(10xx tan 15) = 4000/0.268`
= 14925.37 m
= 14.92 km
संबंधित प्रश्न
Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to
- A,
- B along the direction of string. What is the tension in the string in each case?
A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]
| Lowest Point | Highest Point | |
| a) | mg – T1 | mg + T2 |
| b) | mg + T1 | mg – T2 |
| c) | `mg + T1 –(m_v_1^2)/R` | mg – T2 + (`mv_1^2`)/R |
| d) | `mg – T1 – (mv)/R` | mg + T2 + (mv_1^2)/R |
T1 and v1 denote the tension and speed at the lowest point. T2 and v2 denote corresponding values at the highest point.
Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than that of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.
A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the following figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth h.
In the previous problem, suppose m2 = 2.0 kg and m3 = 3.0 kg. What should be the mass m, so that it remains at rest?
Consider the situation shown in the following figure. Both the pulleys and the string are light and all the surfaces are frictionless.
- Find the acceleration of the mass M.
- Find the tension in the string.
- Calculate the force exerted by the clamp on the pulley A in the figure.
A monkey of mass 15 kg is climbing a rope fixed to a ceiling. If it wishes to go up with an acceleration of 1 m/s2, how much force should it apply on the rope? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling?
Define linear momentum and state its S.I. unit.
A body of mass m moving with a velocity v is acted upon by a force. Write an expression for change in momentum in each of the following cases: (i) When v << c, (ii) When v → c and (iii) When v << c but m does not remain constant. Here, c is the speed of light.
Use Newton's second law of motion to explain the following instance :
A cricketer pulls his hands back while catching a fast moving cricket ball .
The linear momentum of a body of mass m moving with velocity v is :
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : Change in momentum of the body.
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate: The velocity acquired by the body.
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate : The magnitude of the force
State the magnitude and direction of the force of gravity acting on the body of mass 5 kg. Take g = 9.8 m s-2.
A pebble is thrown vertically upwards with a speed of 20 m s-1. How high will it be after 2 s? (Take g = 10 m s-2)
How long will a stone take to fall to the ground from the top of a building 80 m high
The INCORRECT statement about Newton's second law of motion is
A metre scale is moving with uniform velocity. This implies ______.
A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is ______.
