2)a stone of mass 1kg tied to one end of a string of length 1m whirld in a horizontal circle with a costant speed 2 radian/second tension of the string is. A)0.5n b)1n c)2n d)4n 3)the orbital velocity of a satelight close to the earth is v then the orbital velocity at a height 1/4th of earths radius is a)2v/5 b)5v/2 c)2v/{5} d){5}v/2 4)the length of a pendulunm is halvd is energy will a)decreased 2half b)increased to 2 times c)decreased to 1/4th d)increased to 4 times
To solve these physics problems, we will apply relevant equations and principles. Let's break down each question and explain the steps to find the correct answer:
Question 2:
The problem states that a stone of mass 1kg is tied to one end of a string with a length of 1m. The stone is whirled in a horizontal circle at a constant speed of 2 radian/second. We need to find the tension of the string.
To find the tension, we can use the centripetal force equation:
F = (m * v^2) / r
Where:
F is the centripetal force.
m is the mass of the object (1kg in this case).
v is the velocity of the object (2 radian/second in this case).
r is the radius of the circular motion (1m in this case).
Plugging in the given values:
F = (1 * 2^2) / 1
F = 4N
Therefore, the tension in the string is 4 Newtons. So, the correct answer is d) 4N.
Question 3:
The problem states that the orbital velocity of a satellite close to the Earth is v. We need to find the orbital velocity at a height equal to 1/4th of Earth's radius.
To find the orbital velocity at a different height, we can use the conservation of angular momentum equation:
m1 * r1 * v1 = m2 * r2 * v2
Where:
m1 and m2 are the masses of the body (in this case, the satellite), which can be canceled out in this scenario.
r1 and r2 are the distances from the center of the Earth to the satellite (heights).
v1 and v2 are the orbital velocities at heights r1 and r2, respectively.
Let's assume the radius of the Earth is R. Therefore, the height is (1/4) * R.
Using the equation and plugging in the given values:
v1 * R = v2 * (4/5) * R
Simplifying the equation:
v1 = (4/5) * v2
Therefore, the orbital velocity at a height of 1/4th of Earth's radius is (4/5) times the original velocity (v). So, the correct answer is a) 2v/5.
Question 4:
The problem states that the length of a pendulum is halved, and we need to determine what will happen to its energy.
The energy of a pendulum primarily consists of potential energy and kinetic energy. As per the law of conservation of energy, the total mechanical energy remains constant if no external forces act on the system.
When the length of a pendulum is halved, the potential energy (which depends on the height) will decrease. However, since the initial total mechanical energy was conserved, this decrease in potential energy will be compensated by an increase in kinetic energy.
This means that the kinetic energy will increase, so the correct answer is b) increased to 2 times.