Question

A block of mass √3kg rets on a horizontal frictionless XY plane.

What would be the acceleration of the block if it is subjected to
two forces as shown in figure ?

A ) 2.5 msec^-2 y -axis
B) .5ms^-2 along Y-axis
C) 10 msec^-2 along X-axis
D) 15msec^-2 along Y-axis


detailed ans please
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Answer 1

Here you go

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sub to lazarbeam

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Answer 2

Answer:

The acceleration of the block will be 5m/s² along the Y-axis i.e.option(B).

Explanation:

First, let's see the relation between force and acceleration,

$F=Ma$     (1)

Where,

F=net force acting on the block

M=mass of the block=√3kg (given)

a=acceleration of the block

From the question we have,

F₁=10N

F₂=5N

The angle present between the forces (θ)=120°

The net force acting on the block is given as,

$F=\sqrt{F_1^2+F_2^2+2F_1F_2cos\theta}$     (2)

By substituting the values in equation (2) we get;

$F=\sqrt{10^2+5^2+2\times 10\times 5\times cos120\textdegree}$

$F=\sqrt{125-50} =\sqrt{75}$                ($cos120\textdegree=\frac{1}{2}$)

$F=5\sqrt{3} N$    (3)

By substituting the required values in equation (1) we get;

$5\sqrt{3} =\sqrt{3} \times a$

$a=5m/s^2$

Since the 10 N force is more dominating in terms of magnitude then the particle will move along the y-axis.

Hence, the acceleration of the block will be 5m/s² along the Y-axis i.e.option(B).