Applying NLM along 3 Axis

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

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?

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Q.

3 forces are acting on a particle as shown. Find the acceleration of the particle if its mass is 5 kg.

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2. 

3. 

4. 

Q.

Three astronauts, propelled by jet backpacks, push and guide a 2kg asteroid toward a processing dock, exerting the forces shown in figure, with $F_1=4N,F_2=4N,F_3=4N,{\theta }_1={30}^{\circ }and{\theta }_3={60}^{\circ }$. What is the asteroid's acceleration in unit-vector notation ?

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Q.

What is the velocity of block B?

1. 1 m/s in downward direction

2. 2 m/s in upward direction

3. 1 m/s in upward direction

4. 2 m/s in downward direction

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. Zero

4. $g$

Q.

A boy of mass 50 kg is standing on a weighing machine placed on the floor of a lift. The machine reads his weight in newton. What is the reading of the machine when the lift is stationary? Take $g=9.8m{s}^{-2}$

1. 500 N

2. Zero

3. 50 N

4. 490 N

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 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 given figure, pulley is massless and a force $F=10t$ is applied on it. Here, $t$ is time. $[g=10m/s^2]$

1. Time when $4$ kg leaves the ground is $8$ sec.
2. At t = 3 sec, speed of 2 kg is 4 m/s.
3. Power of tension force on 2 kg when 4 kg leaves ground is 800 Watt.
4. Speed of 2 kg when 4 kg leaves ground is 20 m/s.