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Q. No.At \(t = 0,\) a body of mass \(100~\text{g}\) starts moving under the influence of a force \((5\hat{i}+ 10\hat{j})~\text{N}.\) After \(2~\text{s}\) its position is \((2x\hat{i}+5y\hat{j})~\text{m}.\)
The ratio \(x : y\) is:
1. \(1:2\)
2. \(2:5\)
3. \(5:2\)
4. \(5:4\)
The ratio \(x : y\) is:
1. \(1:2\)
2. \(2:5\)
3. \(5:2\)
4. \(5:4\)
Subtopic: Acceleration |
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Level 2: 60%+
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If \(x\) and \(y\) coordinates of a projectile as a function of time \((t)\) are given as \(24t\) and \(43.6t - 4.9t^{2}, \) respectively, then the angle (in degrees) made by the projectile with horizontal when \(t =2~\text{s}\) is:
1. \(60\)
2. \(45\)
3. \(30\)
4. \(75\)
1. \(60\)
2. \(45\)
3. \(30\)
4. \(75\)
Subtopic: Projectile Motion |
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Level 1: 80%+
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A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is \(6.4~\text{m}.\) The speed of bullets from the gun is: (in m/s)
(take \(g = 10~\text{m/s}^2\))
1. \(6.4\)
2. \(8\)
3. \(12\)
4. \(19\)
(take \(g = 10~\text{m/s}^2\))
1. \(6.4\)
2. \(8\)
3. \(12\)
4. \(19\)
Subtopic: Projectile Motion |
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Level 1: 80%+
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The velocity of particle is given as \(\vec{v}=-x \hat{i}+2 y \hat{j}-z \hat{k} ~\text{m/s}.\) The magnitude of acceleration at point \((1,2,4)\) is: (in \(\text{m/s}^2\))
1. \(\sqrt{6}\)
2. \(9\)
3. \(\sqrt{33}\)
4. \(0\)
1. \(\sqrt{6}\)
2. \(9\)
3. \(\sqrt{33}\)
4. \(0\)
Subtopic: Acceleration |
Level 3: 35%-60%
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A car moving with a speed of \(54~\text{km/h}\) takes a turn of radius \(20~\text{m}\). A simple pendulum is suspended from the ceiling of the car. Determined the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10~\text{m/s}^2\))
1. \(\tan ^{-1}(0.5)\)
2. \(\tan ^{-1}(0.75)\)
3. \(\tan ^{-1}(1.125)\)
4. \(\tan ^{-1}(0.25)\)
1. \(\tan ^{-1}(0.5)\)
2. \(\tan ^{-1}(0.75)\)
3. \(\tan ^{-1}(1.125)\)
4. \(\tan ^{-1}(0.25)\)
Subtopic: Circular Motion |
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Level 2: 60%+
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Two identical bodies, projected with the same speed at two different angles cover the same horizontal range \(R\). If the time of these bodies are \(5~\text{s}\) and \(10~\text{s}\), respectively, then the value of \(R\) is: (in m) (Take \(g=10~\text{m/s}^2\))
1. \(250\)
2. \(25\)
3. \(500\)
4. \(125\)
1. \(250\)
2. \(25\)
3. \(500\)
4. \(125\)
Subtopic: Projectile Motion |
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Level 3: 35%-60%
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The two projectiles are projected with the same initial velocities at the \(15^{\circ}\) and \(30^\circ\) with respect to the horizontal. The ratio of their ranges is \(1:x\). The value of \(x\) is:
1. \(\sqrt2\)
2. \(\sqrt3\)
3. \(2\sqrt3\)
4. \(\dfrac{1}{\sqrt2}\)
1. \(\sqrt2\)
2. \(\sqrt3\)
3. \(2\sqrt3\)
4. \(\dfrac{1}{\sqrt2}\)
Subtopic: Projectile Motion |
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Level 1: 80%+
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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: Speed & Velocity |
92%
Level 1: 80%+
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A river of width \(200~\text{m}\) flows from west to east with a speed of \(18~\text{km/h}.\) A boat moves with a speed of \(36~\text{km/h}\) in still water. If the boat makes a round trip from one bank to the opposite bank and back, what are the minimum time taken for the journey and the net displacement along the river bank, respectively?
1. \(20~\text{s}~\text{and}~100~\text{m}~\)
2. \(40~\text{s}~\text{and}~0~\text{m}~\)
3. \(40~\text{s}~\text{and}~200~\text{m}~\)
4. \(40~\text{s}~\text{and}~100~\text{m}~\)
1. \(20~\text{s}~\text{and}~100~\text{m}~\)
2. \(40~\text{s}~\text{and}~0~\text{m}~\)
3. \(40~\text{s}~\text{and}~200~\text{m}~\)
4. \(40~\text{s}~\text{and}~100~\text{m}~\)
Subtopic: Relative Motion |
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Level 2: 60%+
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A projectile is thrown upward at an angle \(60^\circ\) with the horizontal. The speed of the projectile is \(20~\text{m/s}\) when its direction of motion is \(45^\circ\) with the horizontal. The initial speed of the projectile is:
1. \(40\sqrt{2}\) m/s
2. \(40\) m/s
3. \(20\sqrt{3}\) m/s
4. \(20\sqrt{2}\) m/s
1. \(40\sqrt{2}\) m/s
2. \(40\) m/s
3. \(20\sqrt{3}\) m/s
4. \(20\sqrt{2}\) m/s
Subtopic: Projectile Motion |
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Level 2: 60%+
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