Applying NLM along 3 Axis

Q.

A helicopter of mass M is rising vertically upwards with a uniform acceleration a. If the mass of the persons in the helicopter is m, what is the magnitude and direction of the force exerted by the persons on the floor of the helicopter?

1. m(g+a) vertically downwards

2. m(g-a) vertically upwards

3. m(g+a) vertically upwards

4. m(g-a) vertically downwards

Q. In the figure, a force $F=20\text{N}$ is applied on block $\text{A}$. What would be the acceleration of the block $\text{B}$ after $10$ seconds from the start. Assume all surfaces are smooth.

1. $\frac{10}{6}{\text{m/s}}^2$
2. $2{\text{m/s}}^2$
3. zero
4. cannot be calculated

Q. Three charges of unequal magnitudes can remain in equilibrium if arranged on a
$[$Assume two charges of same nature$]$

1. circle
2. triangle
3. None of these
4. straight line

Q. A man of mass $m$ stands on a crate of mass $M$. He pulls on a light rope passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the man on the rope will be

1. $(M+m)g$
2. $\frac{1}{2}(M+m)g$
3. $Mg$
4. $mg$

Q.

A boy wants to climb down a rope. The rope can withstand a maximum tension equal to two-thirds the weight of the boy. If $g$ is the acceleration due to gravity, the minimum acceleration with which the boy should climb down the rope is equal to

1. $\frac{g}{3}$

2. $\frac{2g}{3}$

3. $g$

4. Zero

Q. A block of mass $1\text{kg}$ is at rest relative to a smooth wedge moving leftwards with constant acceleration $a=5{\text{ms}}^{-2}.$ Let $N$ be the normal reaction between the block and the wedge. Take $g=10{\text{ms}}^{-2}$. Choose the correct options from the choices given below:

1. $N=5\sqrt{5}\text{N}$
2. $N=15\text{N}$
3. $\tan \theta =\frac{1}{2}$
4. $\tan \theta =2$

Q.

Two blocks of equal masses $m_1=m_2=3kg$, connected by a light string, are placed on a horizontal surface which is not frictionless. If a force of 20 N is applied in the horizontal direction on a block, the acceleration of each block is $0.5m{s}^{-2}$. Assuming that the frictional forces on the two blocks are equal, the tension in the string will be

1. 10 N

2. 20 N

3. 40 N

4. 60 N

Q. A monkey of mass $40\text{kg}$ climbs up a rope of breaking load $600\text{N}$, hanging from a ceiling. If it climbs up the rope with maximum possible acceleration, then the time taken by the monkey to climb up is:
(Length of the rope is $10\text{m}$ and $g=10{\text{m/s}}^2$).

1. $1\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $2\text{s}$

Q. A body of mass $10\text{kg}$ is acted upon by two perpendicular forces, $6\text{N}$ and $8\text{N}$. The resultant acceleration of the body is

1. $1{\text{ms}}^{–2},$ at an angle of ${\tan }^{–1}\left(\frac{4}{3}\right)$ with respect to $6\text{N}$ force.
2. $0.2{\text{ms}}^{–2},$ at an angle of ${\tan }^{–1}\left(\frac{4}{3}\right)$ with respect to $6\text{N}$ force.
3. $1{\text{ms}}^{–2},$ at an angle of ${\tan }^{–1}\left(\frac{3}{4}\right)$ with respect to $8\text{N}$ force.
4. $0.2{\text{ms}}^{–2},$ at an angle of ${\tan }^{–1}\left(\frac{3}{4}\right)$ with respect to $8\text{N}$ force.

Q. A rod AB is placed inside a hollow spherical shell as shown in figure. A force acts between the rod and the shell to prevent the point B from sliding down and another force at A to prevent it from going up. The number of forces to be shown in FBD of the rod is/are

Q. The system is released from rest with both the springs in unstretched positions. Mass of each block is $1\text{kg}$ and force constant of each spring is $10\text{N/m}$. Extension of horizontal spring in equilibrium is:

1. $0.2\text{m}$
2. $0.4\text{m}$
3. $0.6\text{m}$
4. $0.8\text{m}$

Q. What is the relationship between the three forces?

1. $\frac{F_1}{cos{\theta }_1}=\frac{F_2}{cos{\theta }_2}=\frac{F_3}{cos{\theta }_3}$
2. $\frac{F_1}{sin{\theta }_1}=\frac{F_2}{sin{\theta }_2}=\frac{F_3}{sin{\theta }_3}$
3. $\frac{F_1}{tan{\theta }_1}=\frac{F_2}{tan{\theta }_2}=\frac{F_3}{tan{\theta }_3}$
4. $\frac{F_1}{cot{\theta }_1}=\frac{F_2}{cot{\theta }_2}=\frac{F_3}{cot{\theta }_3}$

Q. Two blocks $A$ and $B$ of same mass $m$ connected by a light spring are suspended by an inextensible string as shown in the figure. Find the magnitude of the acceleration of block $A$ and $B$ just after the string is cut.

1. $2g,0$
2. $0,2g$
3. $g,g$
4. $2g,2g$

Q. Two block of mass $m_A=10\text{kg}$ and $m_B=15\text{kg}$ are connected by a light inextensible string and placed on a smooth horizontal surface as shown in the figure. Find the value of tension force on block $A$, if force applied on block $B$ is $50\sqrt{3}\text{N}$ .

1. $30\text{N}$
2. $45\text{N}$
3. $15\text{N}$
4. $75\text{N}$

Q.

What is the velocity of block B?

1. 1 m/s in downward direction

2. 1 m/s in upward direction

3. 2 m/s in downward direction

4. 2 m/s in upward direction

Q. The blocks $B$ and $C$ in the figure have mass $m$ each. The strings $AB$ and $BC$ are light, having tensions $T_1$ and $T_2$ respectively. The system is in equilibrium with a constant horizontal force $mg$ acting on $C$. Then

1. $\tan {\theta }_1=\frac{1}{2}$
2. $\tan {\theta }_2=1$
3. $T_1=\sqrt{5}mg$
4. $T_2=\sqrt{2}mg$

Q. Sixteen beads in a string are placed on a smooth inclined plane to inclination $\theta =si{n}^{-1}\left(\frac{1}{3}\right)$, such that some of them lie along the incline, whereas the rest hang over the top of the plane. If $N$ beads lie along inclined plane then the acceleration of the bead (of the vertical portion) just below vertex is $\frac{g}{2}$ downwards. Value of $N$ is

Q.

A helicopter is moving to the right at a constant horizontal velocity. It experiences three forces ${\overrightarrow{F}}_{gravitational},{\overrightarrow{F}}_{drag}$ and force on it caused by rotor i.e. ${\overrightarrow{F}}_{rotor}$. Which of the following diagrams can be correct free body diagram representing forces on the helicopter?

1. 

2. 

3. 

4. 

Q. A block of mass $m=2\text{kg}$ on a smooth inclined plane at an angle ${30}^{\circ }$ is connected to a second block of mass $m_2=3\text{kg}$ by a cord passing over a frictionless pulley as shown in fig. The acceleration of each block (in ${\text{m/s}}^2$) is
(assume $g=10{\text{m/sec}}^2$)

Q. The pendulum hanging from the ceiling of a railway carriage makes an angle ${30}^{\circ }$ with the vertical when it is accelerating. The acceleration of the carriage is

1. $\frac{\sqrt{3}}{2}g{\text{m/s}}^2$
2. $\frac{2}{\sqrt{3}}g{\text{m/s}}^2$
3. $g\sqrt{3}{\text{m/s}}^2$
4. $\frac{g}{\sqrt{3}}{\text{m/s}}^2$