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PHXI05:LAWS OF MOTION

363294 An aircraft is moving with uniform velocity $150 m / s$ in space. If all the forces acting on it are balanced, then it will

1 Keep moving with same velocity

2 Remain floating at its place

3 Escape in space

4 Fall down on earth

Explanation:

As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of $150 m / s$ .

MHTCET - 2019

PHXI05:LAWS OF MOTION

363295 If the shown system is in equilibrium, then which of the following options is correct?
supporting img

1

T_{1} = T_{2} \neq T_{3}

2

T_{1} \neq T_{2} = T_{3}

3

T_{1} = T_{2} = T_{3}

4

T_{1} \neq T_{2} \neq T_{3}

Explanation:

The resolution of tensions are shown in the following figure.
supporting img
$T_{3} = W_{2}$ and $T_{3} = T_{2}$ (same rope)
$T_{1} \sin θ = T_{2} \sin θ \Rightarrow T_{1} = T_{2}$
Hence, $T_{1} = T_{2} = T_{3}$

PHXI05:LAWS OF MOTION

363296 A mass $M$ is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
supporting img

1

\sqrt{3} M g

2

\sqrt{2} M g

3

\frac{M g}{\sqrt{3}}

4

\frac{M g}{2}

Explanation:

According to Lami's theorem, $\frac{T_{1}}{\sin 120^{\circ}} = \frac{T_{2}}{\sin 90^{\circ}} = \frac{M g}{\sin 150^{\circ}}$
supporting img
$\frac{2 T_{1}}{\sqrt{3}} = \frac{T_{2}}{1} = 2 M g$ or $T_{1} = \sqrt{3} M g$

PHXI05:LAWS OF MOTION

363297 A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by
supporting img

1

\sqrt{2} M g

2

\sqrt{2} m g

3

g \sqrt{{(M + m)}^{2} + m^{2}}

4

g \sqrt{{(M + m)}^{2} + M^{2}}

Explanation:

Force on the pulley by the clamp
$F = \sqrt{T^{2} + {[(M + m) g]}^{2}}$
$F = \sqrt{{(M g)}^{2} + {[(M + m) g]}^{2}}$
$F = g \sqrt{M^{2} + {(M + m)}^{2}}$

PHXI05:LAWS OF MOTION

363294 An aircraft is moving with uniform velocity $150 m / s$ in space. If all the forces acting on it are balanced, then it will

1 Keep moving with same velocity

2 Remain floating at its place

3 Escape in space

4 Fall down on earth

Explanation:

As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of $150 m / s$ .

MHTCET - 2019

PHXI05:LAWS OF MOTION

363295 If the shown system is in equilibrium, then which of the following options is correct?
supporting img

1

T_{1} = T_{2} \neq T_{3}

2

T_{1} \neq T_{2} = T_{3}

3

T_{1} = T_{2} = T_{3}

4

T_{1} \neq T_{2} \neq T_{3}

Explanation:

The resolution of tensions are shown in the following figure.
supporting img
$T_{3} = W_{2}$ and $T_{3} = T_{2}$ (same rope)
$T_{1} \sin θ = T_{2} \sin θ \Rightarrow T_{1} = T_{2}$
Hence, $T_{1} = T_{2} = T_{3}$

PHXI05:LAWS OF MOTION

363296 A mass $M$ is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
supporting img

1

\sqrt{3} M g

2

\sqrt{2} M g

3

\frac{M g}{\sqrt{3}}

4

\frac{M g}{2}

Explanation:

According to Lami's theorem, $\frac{T_{1}}{\sin 120^{\circ}} = \frac{T_{2}}{\sin 90^{\circ}} = \frac{M g}{\sin 150^{\circ}}$
supporting img
$\frac{2 T_{1}}{\sqrt{3}} = \frac{T_{2}}{1} = 2 M g$ or $T_{1} = \sqrt{3} M g$

PHXI05:LAWS OF MOTION

363297 A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by
supporting img

1

\sqrt{2} M g

2

\sqrt{2} m g

3

g \sqrt{{(M + m)}^{2} + m^{2}}

4

g \sqrt{{(M + m)}^{2} + M^{2}}

Explanation:

Force on the pulley by the clamp
$F = \sqrt{T^{2} + {[(M + m) g]}^{2}}$
$F = \sqrt{{(M g)}^{2} + {[(M + m) g]}^{2}}$
$F = g \sqrt{M^{2} + {(M + m)}^{2}}$

PHXI05:LAWS OF MOTION

363294 An aircraft is moving with uniform velocity $150 m / s$ in space. If all the forces acting on it are balanced, then it will

1 Keep moving with same velocity

2 Remain floating at its place

3 Escape in space

4 Fall down on earth

Explanation:

As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of $150 m / s$ .

MHTCET - 2019

PHXI05:LAWS OF MOTION

363295 If the shown system is in equilibrium, then which of the following options is correct?
supporting img

1

T_{1} = T_{2} \neq T_{3}

2

T_{1} \neq T_{2} = T_{3}

3

T_{1} = T_{2} = T_{3}

4

T_{1} \neq T_{2} \neq T_{3}

Explanation:

The resolution of tensions are shown in the following figure.
supporting img
$T_{3} = W_{2}$ and $T_{3} = T_{2}$ (same rope)
$T_{1} \sin θ = T_{2} \sin θ \Rightarrow T_{1} = T_{2}$
Hence, $T_{1} = T_{2} = T_{3}$

PHXI05:LAWS OF MOTION

363296 A mass $M$ is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
supporting img

1

\sqrt{3} M g

2

\sqrt{2} M g

3

\frac{M g}{\sqrt{3}}

4

\frac{M g}{2}

Explanation:

According to Lami's theorem, $\frac{T_{1}}{\sin 120^{\circ}} = \frac{T_{2}}{\sin 90^{\circ}} = \frac{M g}{\sin 150^{\circ}}$
supporting img
$\frac{2 T_{1}}{\sqrt{3}} = \frac{T_{2}}{1} = 2 M g$ or $T_{1} = \sqrt{3} M g$

PHXI05:LAWS OF MOTION

363297 A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by
supporting img

1

\sqrt{2} M g

2

\sqrt{2} m g

3

g \sqrt{{(M + m)}^{2} + m^{2}}

4

g \sqrt{{(M + m)}^{2} + M^{2}}

Explanation:

Force on the pulley by the clamp
$F = \sqrt{T^{2} + {[(M + m) g]}^{2}}$
$F = \sqrt{{(M g)}^{2} + {[(M + m) g]}^{2}}$
$F = g \sqrt{M^{2} + {(M + m)}^{2}}$

PHXI05:LAWS OF MOTION

363294 An aircraft is moving with uniform velocity $150 m / s$ in space. If all the forces acting on it are balanced, then it will

1 Keep moving with same velocity

2 Remain floating at its place

3 Escape in space

4 Fall down on earth

Explanation:

As all the forces acting on the aircraft are balanced, the net force on it will be zero. Thus, the aircraft will keep moving with the same velocity of $150 m / s$ .

MHTCET - 2019

PHXI05:LAWS OF MOTION

363295 If the shown system is in equilibrium, then which of the following options is correct?
supporting img

1

T_{1} = T_{2} \neq T_{3}

2

T_{1} \neq T_{2} = T_{3}

3

T_{1} = T_{2} = T_{3}

4

T_{1} \neq T_{2} \neq T_{3}

Explanation:

The resolution of tensions are shown in the following figure.
supporting img
$T_{3} = W_{2}$ and $T_{3} = T_{2}$ (same rope)
$T_{1} \sin θ = T_{2} \sin θ \Rightarrow T_{1} = T_{2}$
Hence, $T_{1} = T_{2} = T_{3}$

PHXI05:LAWS OF MOTION

363296 A mass $M$ is hung with light inextensible strings as shown in the figure. The tension in the horizontal string is
supporting img

1

\sqrt{3} M g

2

\sqrt{2} M g

3

\frac{M g}{\sqrt{3}}

4

\frac{M g}{2}

Explanation:

According to Lami's theorem, $\frac{T_{1}}{\sin 120^{\circ}} = \frac{T_{2}}{\sin 90^{\circ}} = \frac{M g}{\sin 150^{\circ}}$
supporting img
$\frac{2 T_{1}}{\sqrt{3}} = \frac{T_{2}}{1} = 2 M g$ or $T_{1} = \sqrt{3} M g$

PHXI05:LAWS OF MOTION

363297 A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by
supporting img

1

\sqrt{2} M g

2

\sqrt{2} m g

3

g \sqrt{{(M + m)}^{2} + m^{2}}

4

g \sqrt{{(M + m)}^{2} + M^{2}}

Explanation:

Force on the pulley by the clamp
$F = \sqrt{T^{2} + {[(M + m) g]}^{2}}$
$F = \sqrt{{(M g)}^{2} + {[(M + m) g]}^{2}}$
$F = g \sqrt{M^{2} + {(M + m)}^{2}}$