Q. No.The velocity at which \(6~\text{kg}\) mass (shown in figure) strikes the ground when it is released from a height of \(6~\text{m}\) above the ground is: (in m/s)
(Assume pulley is massless and string is light and inextensible. (Take \(g = 10~\text{m/s}^{2}\)))
1. \(7.74\)
2. \(7.20\)
3. \(6.55\)
4. \(4.50\)
(Assume pulley is massless and string is light and inextensible. (Take \(g = 10~\text{m/s}^{2}\)))
1. \(7.74\)
2. \(7.20\)
3. \(6.55\)
4. \(4.50\)
Subtopic: Application of Laws |
83%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A wedge \(Y\) with mass of \(10 ~\text {kg}\) and all frictionless surfaces and the inclined surface making \(37^{\circ}\) with horizontal. A block \(X\) with mass \(2 ~\text {kg}\) is placed at the highest point of the wedge as shown in figure is at rest. At \(t=0\) wedge (\(Y\)) is pulled toward right with constant force (\( f\)) of \(24~\text{N}\). Taking the block \(X\) at rest at \(t=0\) the time taken by it to slide down \(8.8~\text{m}\) on the slope, while \( Y\) is on the move, is: (in \(\text{s}\))
(take \(\tan(37^{\circ})=\dfrac{3}{4}\) and \(g= 10~\text {m/s}^2\))
1. \(2\)
2. \(4\)
3. \(\sqrt{2}\)
4. \(2 \sqrt{2}\)
(take \(\tan(37^{\circ})=\dfrac{3}{4}\) and \(g= 10~\text {m/s}^2\))
1. \(2\)
2. \(4\)
3. \(\sqrt{2}\)
4. \(2 \sqrt{2}\)
Subtopic: Application of Laws |
54%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
A small block of mass \(m\) slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration \(a_e\). The angle between the inclined plane and ground is \(\theta\) and its base length is \(L\). Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is:
1. \(\sqrt{\dfrac{2 L}{g \sin 2 \theta-a_0(1+\cos 2 \theta)}} \)
2. \(\sqrt{\dfrac{4 {~L}}{{~g} \sin 2 \theta-{a}_0(1+\cos 2 \theta)}} \)
3. \(\sqrt{\dfrac{4 {~L}}{{~g} \cos ^2 \theta-{a}_0 \sin \theta \cos \theta}}\)
4. \(\sqrt{\dfrac{2 L}{g \sin \theta-a_0 \cos \theta}}\)
1. \(\sqrt{\dfrac{2 L}{g \sin 2 \theta-a_0(1+\cos 2 \theta)}} \)
2. \(\sqrt{\dfrac{4 {~L}}{{~g} \sin 2 \theta-{a}_0(1+\cos 2 \theta)}} \)
3. \(\sqrt{\dfrac{4 {~L}}{{~g} \cos ^2 \theta-{a}_0 \sin \theta \cos \theta}}\)
4. \(\sqrt{\dfrac{2 L}{g \sin \theta-a_0 \cos \theta}}\)
Subtopic: Application of Laws |
62%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A body of mass m is suspended by two strings making angles \(\theta _1\) and \(\theta _2\) with the horizontal ceiling with tensions \(T_1\) and \(T_2\) simultaneously. \(T_1\) and \(T_2\) are related by \(T_1 = \sqrt{3} ~T_2,\) then the angles \(\theta _1\) and \(\theta _2\) are:
| 1. | \(\theta_1=30^{\circ}, \theta_2=60^{\circ} \text { with } T_2=\dfrac{4 mg}{5}\) |
| 2. | \(\theta_1=30^{\circ}, \theta_2=60^{\circ} \text { with } T_2=\dfrac{3 {mg}}{4}\) |
| 3. | \(\theta_1=60^{\circ}, \theta_2=30^{\circ} \text { with } T_2=\dfrac{mg}{2}\) |
| 4. | \(\theta_1=45^{\circ}, \theta_2=45^{\circ} \text { with } T_2=\dfrac{3mg}{4}\) |
Subtopic: Application of Laws |
81%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A body of mass \(1 ~\text{kg}\) is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions \(T_1\) and \(T_2,\) respectively, are (in \(\text{N}\)): (Take acceleration due to gravity \(10 ~\text{m/s}^2 \))
1. \(5,5\)
2. \(5,5\sqrt3 ~\)
3. \(5\sqrt3,5\sqrt3 ~\)
4. \(5\sqrt3,5 ~\)
1. \(5,5\)
2. \(5,5\sqrt3 ~\)
3. \(5\sqrt3,5\sqrt3 ~\)
4. \(5\sqrt3,5 ~\)
Subtopic: Application of Laws |
86%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A light unstretchable string passing over a smooth light pulley connects two blocks of masses \(m_1\) and \(m_2\). If the acceleration of the system is \(g/8\), then the ratio of the masses \(m_2\)/\(m_1\) is :
1. \(4:3\)
2. \(5:3\)
3. \(8:1\)
4. \(9:7\)
Subtopic: Application of Laws |
86%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A body of weight \(200\) N is suspended from a tree branch through a chain of mass \(10\) kg. The branch pulls the chain by a force equal to (if \(g=10 \mathrm{~m} / \mathrm{s}^2\)) :
1. \(300\) N
2. \(150\) N
3. \(100\) N
4. \(200\) N
Subtopic: Application of Laws |
82%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A light string passing over a smooth light pulley connects two blocks of masses \(\text{m}_1\) and \(\text{m}_2\) (where \(\text{m}_2>\text{m}_1\)). If the acceleration of the system is \(\text g/\sqrt 2\) , then the ratio of the masses \(\text{m}_1/\text{m}_2\) is:
1. \(\frac{\sqrt{3}+1}{\sqrt{2}-1}\)
2. \(\frac{1+\sqrt{5}}{\sqrt{2}-1}\)
3. \(\frac{1+\sqrt{5}}{\sqrt{5}-1}\)
4. \(\frac{\sqrt{2}-1}{\sqrt{2}+1}\)
1. \(\frac{\sqrt{3}+1}{\sqrt{2}-1}\)
2. \(\frac{1+\sqrt{5}}{\sqrt{2}-1}\)
3. \(\frac{1+\sqrt{5}}{\sqrt{5}-1}\)
4. \(\frac{\sqrt{2}-1}{\sqrt{2}+1}\)
Subtopic: Application of Laws |
85%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
Two forces
\({\overrightarrow {F}_1=(6 \hat{i}+3 \hat{j}+\hat{k}) ~\text N,~\text{and}~\overrightarrow{F}_2=(2 \hat{i}+\hat{j}+3 \hat{k}) ~\text N}\) act simultaneously on a particle of mass \(4~\text{kg}.\) What is the magnitude of the particle’s acceleration?
\({\overrightarrow {F}_1=(6 \hat{i}+3 \hat{j}+\hat{k}) ~\text N,~\text{and}~\overrightarrow{F}_2=(2 \hat{i}+\hat{j}+3 \hat{k}) ~\text N}\) act simultaneously on a particle of mass \(4~\text{kg}.\) What is the magnitude of the particle’s acceleration?
| 1. | \({\sqrt{10}~\text{m/s}^2} \) | 2. | \({\sqrt{6}~\text{m/s}^2}\) |
| 3. | \({\sqrt{3}~\text{m/s}^2}\) | 4. | \({\sqrt{2}~\text{m/s}^2}\) |
Subtopic: Application of Laws |
78%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
The acceleration of the \(2~\text{kg}\) block is shown in the diagram is: (neglect friction)
1. \(\frac{4g}{15}\)
2. \( \frac{2g}{15}\)
3. \(\frac{g}{15}\)
4. \( \frac{2g}{3}\)
1. \(\frac{4g}{15}\)
2. \( \frac{2g}{15}\)
3. \(\frac{g}{15}\)
4. \( \frac{2g}{3}\)
Subtopic: Application of Laws |
55%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
© 2026 GoodEd Technologies Pvt. Ltd.