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Q. No.The machine as shown has \(2\) rods of length \(1~\text{m}\) connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a \(2~\text{kg}\) weight moves up and down. If the roller is moving towards the right at a constant speed, the weight moves up with a:
| 1. | speed which is \(\frac{3}{4}\text{th}\) of that of the roller when the weight is \(0.4~\text{m}\) above the ground |
| 2. | constant speed |
| 3. | decreasing speed |
| 4. | increasing speed |
Subtopic: Â Speed & Velocity |
Level 4: Below 35%
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A particle is moving with a velocity \(\vec v=K(y \hat{i}+x\hat{j}),\) where \(K\) is a constant. The general equation for its path is:
1. \(y=x^2+\text{constant}\)
2. \(y^2=x+\text{constant}\)
3. \(y^2=x^2+\text{constant}\)
4. \(xy=\text{constant}\)
1. \(y=x^2+\text{constant}\)
2. \(y^2=x+\text{constant}\)
3. \(y^2=x^2+\text{constant}\)
4. \(xy=\text{constant}\)
Subtopic: Â Speed & Velocity |
 65%
Level 2: 60%+
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A particle has an initial \((t = 0)\) velocity \(\vec{u}=5 \hat{i}\) and is at its origin at this instant. Its acceleration is given by \((3\hat{i}+4\hat{j}).\) When the particles \(x\) co-ordinate is \(16\) units, then its speed is:
1. \(13\) units
2. \(\sqrt{161}\) units
3. \(12\) units
4. \(\sqrt{185}\) units
1. \(13\) units
2. \(\sqrt{161}\) units
3. \(12\) units
4. \(\sqrt{185}\) units
Subtopic: Â Speed & Velocity |
 69%
Level 2: 60%+
JEE
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The displacement of a particle changes with time as \({x}=6 t^3-12 t^2+20 t+30.\) The velocity of the particle when its acceleration becomes zero (\(t\) is time in \(\text s\)) is:
1. \(12~\text{m/s}\)
2. \(14~\text{m/s}\)
3. \(18~\text{m/s}\)
4. \(20~\text{m/s}\)
1. \(12~\text{m/s}\)
2. \(14~\text{m/s}\)
3. \(18~\text{m/s}\)
4. \(20~\text{m/s}\)
Subtopic: Â Speed & Velocity |
 86%
Level 1: 80%+
JEE
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The position of a particle in a three-dimensional coordinate system is described by:
\({x=a\cos \omega t},~{y=a\sin \omega t}~\text{and},~{z=a \omega t},\)
where \(a\) and \(\omega\) are constants. The speed of the particle is:
| 1. | \({\sqrt{2}a \omega}\) | 2. | \({a \omega}\) |
| 3. | \({\sqrt{3}a \omega}\) | 4. | \({{2}a \omega}\) |
Subtopic: Â Speed & Velocity |
Level 3: 35%-60%
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A \(4~\text{kg}\) mass moves under the influence of a force \(\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right)~ \text{N}\) where \(t\) is the time in second. If mass starts from origin at \(t=0\), the velocity and position after \(t = 2~\text{s}\) will be:
1. \(\vec{v}=3 \hat{i}+\dfrac{3}{2} \hat{j} ~~~\vec{r}=\dfrac{6}{5} \hat{i}+\hat{j}\)
2. \(\vec{v}=4 \hat{i}-\dfrac{3}{2} \hat{j}~~~~ \vec{r}=\dfrac{8}{5} \hat{i}-\hat{j}\)
3. \(\vec{v}=4 \hat{i}+\dfrac{5}{2} \hat{j} ~~~~\vec{r}=\dfrac{8}{5} \hat{i}+2 \hat{j}\)
4. \(\vec{v}=4 \hat{i}-\dfrac{3}{2} \hat{j} ~~~~\vec{r}=\dfrac{6}{5} \hat{i}-\hat{j}\)
1. \(\vec{v}=3 \hat{i}+\dfrac{3}{2} \hat{j} ~~~\vec{r}=\dfrac{6}{5} \hat{i}+\hat{j}\)
2. \(\vec{v}=4 \hat{i}-\dfrac{3}{2} \hat{j}~~~~ \vec{r}=\dfrac{8}{5} \hat{i}-\hat{j}\)
3. \(\vec{v}=4 \hat{i}+\dfrac{5}{2} \hat{j} ~~~~\vec{r}=\dfrac{8}{5} \hat{i}+2 \hat{j}\)
4. \(\vec{v}=4 \hat{i}-\dfrac{3}{2} \hat{j} ~~~~\vec{r}=\dfrac{6}{5} \hat{i}-\hat{j}\)
Subtopic: Â Speed & Velocity |
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