If four balloons A, B, C and D are filled with hydrogen, oxygen, helium and nitrogen gases respectively and left in air, which balloon reaches to the highest distance from the Earth?
Mechanics
22. To start your loaded trolley bag, you exert more force than when it is
To start your loaded trolley bag, you exert more force than when it is moving. This is an example of
– Static friction opposes the start of motion and is generally greater than kinetic friction, which opposes motion while it is occurring.
– Overcoming inertia and static friction requires more force than overcoming kinetic friction to maintain motion.
23. ‘Hydraulic brakes’ and ‘Hydraulic lift’ are devices in which fluids ar
‘Hydraulic brakes’ and ‘Hydraulic lift’ are devices in which fluids are used for transmitting
24. X is twice as massive as Y. X also runs twice faster than Y. Which one
X is twice as massive as Y. X also runs twice faster than Y. Which one among the following is the ratio of kinetic energy of X and Y ?
KE_X = ½ * m_X * v_X² = ½ * (2 * m_Y) * (2 * v_Y)² = ½ * 2 * m_Y * 4 * v_Y² = 8 * (½ * m_Y * v_Y²)
KE_Y = ½ * m_Y * v_Y²
The ratio KE_X / KE_Y = [8 * (½ * m_Y * v_Y²)] / [½ * m_Y * v_Y²] = 8 / 1. Thus, the ratio is 8:1.
25. The Earth travels on its orbit at a speed of approximately 4400 km per
The Earth travels on its orbit at a speed of approximately 4400 km per hour. Why do we not feel this high speed ?
– In physics, we typically feel acceleration (changes in speed or direction), not constant velocity. Since our velocity relative to the Earth’s surface (for the orbital motion) is zero and remains zero, we don’t feel the orbital speed.
– This is related to the concept of inertial frames of reference. We are in the same inertial frame as the Earth’s surface for this motion.
26. The following figure shows the displacement time (x-t) graph of a body
The following figure shows the displacement time (x-t) graph of a body in motion. The ratio of the speed in first second and that in next two seconds is :
In the first second (from t=0 to t=1), the displacement changes from 0 to 3. The velocity is `(3 – 0) / (1 – 0) = 3/1 = 3` units/second. The speed in the first second (v1) is `|3| = 3`.
In the next two seconds (from t=1 to t=3), the displacement changes from 3 to 0. The velocity is `(0 – 3) / (3 – 1) = -3/2` units/second. The speed in the next two seconds (v2) is `|-3/2| = 3/2`.
The ratio of the speed in the first second and that in the next two seconds is `v1 : v2 = 3 : (3/2)`. To express this ratio in integers, we can multiply both parts by 2: `(3 * 2) : (3/2 * 2) = 6 : 3`. Dividing by 3, we get the simplified ratio `2 : 1`.
27. A person moves along a circular path by a distance equal to half the c
A person moves along a circular path by a distance equal to half the circumference in a given time. The ratio of his average speed to his average velocity is :
The distance covered by the person is half the circumference, $d = \frac{1}{2} C = \pi R$.
Let the time taken be $t$.
Average speed is defined as the total distance traveled divided by the total time taken.
Average speed = $\frac{d}{t} = \frac{\pi R}{t}$.
The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point.
Let the starting point be A and the ending point be B, where AB is a diameter of the circle.
The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter.
Displacement = $2R$.
Average velocity is defined as the total displacement divided by the total time taken.
Average velocity = $\frac{\text{Displacement}}{t} = \frac{2R}{t}$.
The ratio of average speed to average velocity is:
Ratio = $\frac{\text{Average speed}}{\text{Average velocity}} = \frac{\pi R / t}{2R / t} = \frac{\pi R}{t} \times \frac{t}{2R} = \frac{\pi}{2}$.
The value $\frac{\pi}{2}$ is equivalent to $0.5\pi$.
28. The explanation of, why we get thrown back with a jerk when the statio
The explanation of, why we get thrown back with a jerk when the stationary bus we are sitting in starts moving forward is given by :
29. The figure given below shows the direction of the two forces P and Q a
The figure given below shows the direction of the two forces P and Q acting on a skydiver :
Let’s analyze the options:
A) Force P is caused by the gravity and force Q is caused by the friction. This statement correctly identifies the source of the forces. P is gravity, and Q is air resistance, which is a form of fluid friction. This statement is correct.
B) When the force P is bigger than the force Q, the speed of the skydiver remains the same. If P > Q, there is a net downward force (P – Q). According to Newton’s Second Law (F_net = ma), this net force causes acceleration in the downward direction, meaning the speed will increase, not remain the same. This statement is incorrect.
C) After the parachute opens, force P remains the same while force Q increases. Force P is gravity (mg), which depends on the skydiver’s mass and the acceleration due to gravity. Opening a parachute does not significantly change the skydiver’s mass or gravity. Thus, P remains essentially the same. Air resistance (Q) depends on the skydiver’s speed, the density of the air, and the skydiver’s shape and size (drag coefficient and area). Opening a parachute dramatically increases the surface area and drag coefficient, causing the air resistance force Q to increase significantly at the same speed. This statement is correct.
D) After the parachute opens, force P decreases while force Q increases. As explained above, P (gravity) remains essentially the same. Q increases dramatically. This statement is incorrect because it says P decreases.
Both A and C are factually correct statements about the forces. However, MCQs typically have a single best answer. Option C describes a crucial dynamic event in skydiving (parachute deployment) and its direct impact on the forces and resulting motion, which is a common physics concept tested. Option A is a static identification of the forces. Given the options and the nature of physics questions regarding skydiving, Option C is likely considered the intended answer as it addresses a key change in the system’s dynamics.