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 <img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528352838-3.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">

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

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

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

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

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

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

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

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

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

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

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

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

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is

$$\frac{{{\text{b}}{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

$$\frac{{{{\text{d}}^2}}}{{12\overline {\text{x}} }} + \overline {\text{x}} $$

$$\frac{{{{\text{b}}^2}}}{{12}} + \overline {\text{x}} $$

$$\frac{{{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

A body A of mass 6.6 kg which is lying on a horizontal platform 4.5 m from its edge is connected to the end of a light string whose other end is supporting a body of mass 3.2 kg as shown in below figure. If the friction between the platform and the body A is $$\frac{1}{3}$$, the acceleration is

0.5 m/sec2

0.75 m/sec2

1.00 m/sec2

1.25 m/sec2

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

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

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

When a body of mass M₁ is hanging freely and another of mass M₂ lying on a smooth inclined plane ($$\alpha $$) are connected by a light index tensile string passing over a smooth pulley, the acceleration of the body of mass M₁, will be given by

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

$$\frac{{{\text{g}}\left( {{{\text{M}}_1} - {{\text{M}}_2}\sin \alpha } \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}{\text{m/se}}{{\text{c}}^2}$$

$$\frac{{{\text{g}}\left( {{{\text{M}}_2} + {{\text{M}}_1}\sin \alpha } \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}{\text{m/se}}{{\text{c}}^2}$$

$$\frac{{{\text{g}}\left( {{{\text{M}}_2} \times {{\text{M}}_1}\sin \alpha } \right)}}{{{{\text{M}}_2} - {{\text{M}}_1}}}{\text{m/se}}{{\text{c}}^2}$$

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.

The moment of inertia of the resulting body about Y-axis is

$$\frac{{\pi \rho {R^5}}}{4}$$

$$\frac{{5\pi \rho {R^5}}}{{12}}$$

$$\frac{{7\pi \rho {R^5}}}{{12}}$$

$$\frac{{3\pi \rho {R^5}}}{4}$$