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 <img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528352952-2.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">

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:

A

50 kg

B

75 kg

C

25 kg

D

60 kg

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

A

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

B

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

C

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

D

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

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.

A

Increase

B

Decrease

C

Not be effected

D

None of these

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

A

Same

B

Half

C

Double

D

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

A

Same

B

Half

C

Double

D

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

A

50 kg

B

750 kg

C

100 kg

D

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.

A

Will

B

Will not

C

Either A or B

D

None of these

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

A

0.5 m/sec2

B

0.75 m/sec2

C

1.00 m/sec2

D

1.25 m/sec2

A mass m is constrained to move on a horizontal frictionless surface. It is set in circular motion with radius r₀ and angular speed ω₀ by an applied force $$\overrightarrow {\bf{F}} $$ communicated through an inextensible thread that passesthrough a hole on the surface as shown in figure given below. Then, this force is suddenly doubled.

The magnitude of the radial velocity of the mass

A

increases till mass falls into hole

B

decreases till mass falls into hole

C

remains constant

D

becomes zero at radius r1, where 0 1 0

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

A

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

B

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

C

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

D

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