In the shown figure, the tension (T) in the string will be<br><img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528353569-2.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}{\text{g}}}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

$$\frac{{2{{\text{m}}_1}{{\text{m}}_2}{\text{g}}}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

$$\frac{{{{\text{m}}_1} + {{\text{m}}_2}}}{{{{\text{m}}_1}{{\text{m}}_2}{\text{g}}}}$$

$$\frac{{{{\text{m}}_1} + {{\text{m}}_2}}}{{2{{\text{m}}_1}{{\text{m}}_2}{\text{g}}}}$$

Correct Answer: $$\frac{{2{{\text{m}}_1}{{\text{m}}_2}{\text{g}}}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

A block of mass m₁, placed on an inclined smooth plane is connected by a light string passing over a smooth pulley to mass m₂, which moves vertically downwards as shown in the below figure. The tension in the string is

$$\frac{{{{\text{m}}_1}}}{{{{\text{m}}_2}}}$$

$${{\text{m}}_1}{\text{g}}\sin \alpha $$

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}{\text{g}}\left( {1 + \sin \alpha } \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

A block of mass 20 kg lying on a rough horizontal plane is connected by a light string passing over a smooth pulley to another mass 5 kg, which can move freely in the Vertical direction, as shown in the below figure. The tension in the string will ___________ with the increase in coefficient of friction.

Increase

Decrease

Not be effected

None of these

A weight of 100 kg is supported by a string whose ends are attached to pegs ‘A’ and ‘B’ at the same level shown in below figure. The tension in the string is

50 kg

750 kg

100 kg

120 kg

Two blocks ‘A’ and ‘B’ of masses 150 kg and 50 kg respectively are connected by means of a string as shown in the below figure. The tension in all the three strings __________ be same.

Will

Will not

Either A or B

None of these

If the masses of both the bodies, as shown in the below figure, are reduced to 50 percent, then tension in the string will be

Same

Half

Double

None of these

Two loads of 50 kg and 75 kg are hung at the ends of a rope passing over a smooth pulley shown in below figure. The tension in the string is:

50 kg

75 kg

25 kg

60 kg

The force induced in the string BC due to the load 'W' as shown in the below figure is

W sinθ

W cosθ

W tanθ

W cotθ

Two bodies of masses m₁ and m₂ are hung from the ends of a rope, passing over a frictionless pulley as shown in the figure below. The acceleration of the string will be

$$\frac{{{\text{g}}\left( {{{\text{m}}_1} - {{\text{m}}_2}} \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

$$\frac{{2{\text{g}}\left( {{{\text{m}}_1} - {{\text{m}}_2}} \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

$$\frac{{{\text{g}}\left( {{{\text{m}}_1} + {{\text{m}}_2}} \right)}}{{{{\text{m}}_1} - {{\text{m}}_2}}}$$

$$\frac{{2{\text{g}}\left( {{{\text{m}}_1} + {{\text{m}}_2}} \right)}}{{{{\text{m}}_1} - {{\text{m}}_2}}}$$

The force induced in the string AB due to the load W, as shown in the below figure is

W sinθ

W cosθ

W secθ

W cosecθ

If the masses of both the bodies, as shown in the below figure, are doubled, then the acceleration in the string will be

Same

Half

Double

None of these