Advertisements
Advertisements
Question
In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle's motion. A particle of mass m projected upward takes time t1 in reaching the maximum height and t2 in the return journey to the original point. Then.
Options
t1 < t2
t1 > t2
t1 = t2
the relation between t1 and t2 depends on the mass of the particle
Advertisements
Solution
t1 > t2
Let acceleration due to air resistance force be a.
Let H be maximum height attained by the particle.
Direction of air resistance force is in the direction of motion.
In the upward direction of motion,
\[a_{eff} = \left| g - a \right|\]
\[t_1 = \sqrt{\frac{2H}{\left| g - a \right|}} . . . (1)\]
In the downward direction of motion,
\[a_{eff} = g + a\]
\[t_2 = \sqrt{\frac{2H}{g + a}} . . . (2)\]
So, t1 > t2.
APPEARS IN
RELATED QUESTIONS
A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because ______.
Name the scientist who gave the laws of motion.
Fill in the following blank with suitable word :
Newton’s first law of motion is also called Galileo’s law of ………………………
Find the acceleration produced by a force of 5 N acting on a mass of 10 kg.
A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration 'a' along a straight horizontal track , the string supporting the bob makes an angle tan−1 (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity. If the angle of incline is tan−1 (a/g), the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerating on a horizontal straight track or moving on an incline? If yes, how? If not, then suggest a method to do so.
Neglect the effect of rotation of the earth. Suppose the earth suddenly stops attracting objects placed near its surface. A person standing on the surface of the earth will.
Three rigid rods are joined to form an equilateral triangle ABC of side 1 m. Three particles carrying charges 20 μC each are attached to the vertices of the triangle. The whole system is at rest in an inertial frame. The magnitude of the resultant force on the charged particle at A is.
A block of mass 2 kg placed on a long frictionless horizontal table is pulled horizontally by a constant force F. It is found to move 10 m in the first seconds. Find the magnitude of F.
An object of mass 2 kg is sliding with a constant velocity of 4 m/s on a frictionless horizontal table. The force required to keep this object moving with the same velocity is :
Give qualitative definition of force on the basic of Newton's first law of motion.
Explain the following :
After alighting from a moving bus , one has to run for some distance in the direction of bus in order to avoid falling .
Derive the relation between newton and dyne.
Give one example each of inertia of rest and inertia of motion.
Give two examples of the following:
Inertia of motion
Match the following
| Column I | Column II |
| Newton’s I law | propulsion of a rocket |
| Newton’s II law | Stable equilibrium of a body |
| Newton’s III law | Law of force |
| Law of conservation of linear momentum | Flying nature of bird |
Classify the types of force based on their application.
A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).
If the net force on an object is zero, what happens?
An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is ______. (g = 10 ms−2)
