A person travelling in a straight line moves with a constant velocity \(v_1\) for a certain distance \(x\) and with a constant velocity \(v_2\) for the next equal distance. The average velocity \(v\) is given by the relation:
1. | \(\frac{1}{v} = \frac{1}{v_1}+\frac{1}{v_2}\) | 2. | \(\frac{2}{v} = \frac{1}{v_1}+\frac{1}{v_2}\) |
3. | \(\frac{v}{2} = \frac{v_1+v_2}{2}\) | 4. | \(v = \sqrt{v_1v_2}\) |
A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time if the elevator is moving uniformly and time if the elevator is stationary. Then:
1. | \(t_1<t_2 \) or \(t_1>t_2 \) depending upon whether the lift is going up or down. |
2. | \(t_1<t_2 \) |
3. | \(t_1>t_2 \) |
4. | \(t_1=t_2 \) |
A ball is thrown vertically downwards with a velocity of \(20\) m/s from the top of a tower. It hits the ground after some time with the velocity of \(80\) m/s . The height of the tower is: (assuming \(g = 10~\text{m/s}^2)\)
1. | \(340\) m | 2. | \(320\) m |
3. | \(300\) m | 4. | \(360\) m |
A person sitting on the ground floor of a building notices through the window, of height \(1.5~\text{m}\), a ball dropped from the roof of the building crosses the window in \(0.1~\text{s}\). What is the velocity of the ball when it is at the topmost point of the window? \(\left(g = 10~\text{m/s}^2\right )\)
1. | \(15.5~\text{m/s}\) | 2. | \(14.5~\text{m/s}\) |
3. | \(4.5~\text{m/s}\) | 4. | \(20~\text{m/s}\) |
A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is:
1. | \(\dfrac{2n+1}{2n-1}\) | 2. | \(\dfrac{2n}{2n-1}\) |
3. | \(\dfrac{2n-1}{2n}\) | 4. | \(\dfrac{2n-1}{2n+1}\) |
1. | \(1: \sqrt{3}\) | 2. | \(\sqrt{3}: 1\) |
3. | \(1:1\) | 4. | \(1:2\) |
1. | \(1:1:1:1\) | 2. | \(1:2:3:4\) |
3. | \(1:4:9:16\) | 4. | \(1:3:5:7\) |
A stone is thrown vertically downwards with an initial velocity of \(40\) m/s from the top of a building. If it reaches the ground with a velocity of \(60\) m/s, then the height of the building is: (Take \(g=10\) m/s2)
1. | \(120\) m | 2. | \(140\) m |
3. | \(80\) m | 4. | \(100\) m |
The figure given below shows the displacement and time, \((x\text -t)\) graph of a particle moving along a straight line:
The correct statement, about the motion of the particle, is:
1. | the particle moves at a constant velocity up to a time \(t_0\) and then stops. |
2. | the particle is accelerated throughout its motion. |
3. | the particle is accelerated continuously for time \(t_0\) then moves with constant velocity. |
4. | the particle is at rest. |
1. | 2. | ||
3. | 4. |