Laws of Motion Test

Result

Laws of Motion Test - 77

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Question 1
1 / -0

A 10 kg block is pulled a along a frictional surface in the form of an are of a circle of radius 10 m. The applied force F is 200 N as shown in figure If a block started from rest at P

A
the velocity at Q would be 20 m/s

B
the velocity at Q would be 17 m/s

C
the velocity at Q would be 15 .5 m.s

D
the velocity at Q would be 18 m/s

Solution

We know,
change in KE $$=$$ work done
$$(KE)_f-(KE)_i=F$$(length of arc)
$$(KE)_f-O=F\times 60^o\times \dfrac{\pi}{80^o}\times$$ (radius) [Initially at rest]
$$(KE)_f=\dfrac{\pi F}{3}\times 10$$
$$(KE)_f=\dfrac{\pi\times 200}{3}\times 10$$
$$\dfrac{1}{2}mv^2_f=\dfrac{2000\pi}{3}$$
$$v^2_f=\dfrac{2}{m}\times \dfrac{2000\pi}{3}$$
$$v_f=\sqrt{\dfrac{2}{10}\times \dfrac{2000\pi}{3}}$$
$$v_f\approx 20m/s$$,
Question 2
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The variation of force F acting on a body moving along x-axis varies with its position (x) shown in figure.
The body is in stable equilibrium state at

A
P

B
Q

C
R

D
both P & Q

Solution
Question 3
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A heavy particle hanging from a fixed point by a light inextensible string of length l h projected horizontally with a speed of $$\sqrt { { g }^{ l } } $$. Find the speed of the particle and the inclination of the string to the vertical at the instant of the motion, when the tension in the string is equal to the weight of the particle.

A
$$\sqrt { gl } $$

B
$$\sqrt { 2gl } $$

C
$$\sqrt { 3gl } $$

D
$$\sqrt { \frac { gl }{ 3 } } $$

Solution
Question 4
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A car is circulating on a circular path of radius r. At some instant its velocity is v and rate of increase of speed is a. The resultant acceleration of the car will be

A
$$\sqrt { \dfrac { { v }^{ 2 } }{ { a }^{ 2 } } +{ r }^{ 2 } } $$

B
$$\sqrt { \dfrac { { v }^{ 2 } }{ r } +a } $$

C
$$\sqrt { \dfrac { { v }^{ 4 } }{ { r }^{ 2 } } +{ a }^{ 2 } } $$

D
$$\left( { \dfrac { { v }^{ 2 } }{ { r }^{ } } +{ a }^{ } } \right) $$

Solution
Question 5
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Which of the following sets of concurrent forces may be in equilibrium?

A
$$F_1=3N, F_2=5N, F_3=1N$$

B
$$F_1=3N, F_2=5N, F_3=9N$$

C
$$F_1=3N, F_2=5N, F_3=6N$$

D
$$F_1=3N, F_2=5N, F_3=15N$$

Solution
Question 6
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A particle located in the one-dimensional potential field has potential energy function $$U(x) = \dfrac{a}{{{x^2}}} - \dfrac{b}{{{x^3}}}$$ where a and b are positive constants. The position of equilibrium corresponds to x?

A
$$\dfrac{{3a}}{{2b}}$$

B
$$\dfrac{{2b}}{{3a}}$$

C
$$\dfrac{{2a}}{{3b}}$$

D
$$\dfrac{{3b}}{{2a}}$$

Solution
Question 7
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A strign of length $$1=1m$$ is fixed at one end and carries a mass of $$100gm$$ at other end. The string makes $$\sqrt { 5 } \pi$$ revolutions per second about a vertical axis passing through its second end. What is the angle of inclination of the string with the vertical?

A
$$30^0$$

B
$$45^0$$

C
$$60^0$$

D
$$75^0$$

Solution
Question 8
1 / -0

$$F = 2 {x^2} - 3x-2$$. Choose correct option

A
$$x= -\dfrac{1}{2}$$ is position of stable equilibrium

B
$$x= 2$$ is position of stable equilibrium

C
$$x= -\dfrac{1}{2}$$ is position of unstable equilibrium

D
$$x= 2$$ is position of neutral equilibrium

Solution
Question 9
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A uniform rod of mass $$M$$ has an impulse applied at right angles to one end begins to move with speed $$V$$,the magnitude of the impulse is

A
$$MV$$

B
$$\dfrac {MV}{2}$$

C
$$3MV$$

D
$$\dfrac {2MV}{3}$$
Question 10
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A bucket tied at the end of a $$1.6m$$ long string is whirled in a vertical circle with a constant speed. What should be the minimum speed so that the water from the bucket does not spill when the bucket is at the highest position, (Take g=10m/s^2$$)

A
$$16m/s$$

B
$$6.25m/s$$

C
$$4m/s$$

D
$$2m/s$$

Solution