Q. No.| 1. | \(5~\text{m}\) | 2. | \(25~\text{m}\) |
| 3. | \(45~\text{m}\) | 4. | \(58~\text{m}\) |
| 1. | \(68\) m | 2. | \(56\) m |
| 3. | \(60\) m | 4. | \(64\) m |
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
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. | \(\dfrac{2n-1}{2n+1}\) |
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 stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:
| 1. | \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
| 2. | \(h_2=3h_1\) and \(h_3=3h_2\) |
| 3. | \(h_1=h_2=h_3\) |
| 4. | \(h_1=2h_2=3h_3\) |
A particle has initial velocity \(\left(2 \hat{i} + 3 \hat{j}\right)\) and acceleration \(\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)\). The magnitude of velocity after \(10\) s will be:
1. \(9 \sqrt{2}~ \text{units}\)2. \(5 \sqrt{2} ~\text{ units}\)
3. \(5~\text{units}\)
4. \(9~\text{units}\)
| 1. | 20 m/s | 2. | 40 m/s |
| 3. | 5 m/s | 4. | 10 m/s |
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