Laws of Motion Test

Result

Laws of Motion Test - 74

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Question 1
1 / -0

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $$L$$ from one end of the rod. The rod is set in angular motion about a vertical axis passing through A with a constant angular acceleration $$\alpha $$. The friction coefficient between the rod and the bead is $$\mu $$.Neglecting gravity, what is the time after which the bead starts slipping on the rod.

A
$$\sqrt {\frac{\mu }{\alpha }} $$

B
$$\frac{\mu }{{\sqrt \alpha }}$$

C
$$\sqrt {\frac{1}{{\mu \alpha }}} $$

D
$$\frac{1}{\mu }\sqrt {\frac{1}{\alpha }} $$

Solution
Question 2
1 / -0

A mass of $$6\ kg$$ is suspended by a rope of length $$2\ m$$ from a ceiling. A force of $$50\ N$$ is applied in horizontal direction at the mid point of the rope. What is the angle between the rope and the vertical in equilibrium.

A
$$\tan^{-1} \left(\dfrac{4}{5} \right)$$

B
$$\tan^{-1} \left(\dfrac{5}{4} \right)$$

C
$$\tan^{-1} \left(\dfrac{5}{6} \right)$$

D
None

Solution
Question 3
1 / -0

Four point charges are placed in a straight line with magnitude and separation as shown in the diagram. What should be the value of $${q_0}$$ such that $$ + 10\mu C\;ch\arg e$$ is in equlibrium?

A
-80 $$\mu C$$

B
+ 40 $$\mu C$$

C
+80 $$\mu C$$

D
-20 $$\mu C$$

Solution
Question 4
1 / -0

For a paticle in a vertically circle with unifrom speed, the maximum and minimum tension in the string are in the ratio 5 : 3, if the radius of vertical circle is 2 m, the speed of revolving body is $$ ( g= 10 m/s^2) $$

A
$$ \sqrt {5} m/s $$

B
$$ 4 \sqrt {5} m/s $$

C
$$ 5 m/s $$

D
$$ 10 m/s $$

Solution
Question 5
1 / -0

A road is banked at an angle of $$37^{ 0 }.$$ If a car moving at 54 km/hr does not experience any friction force while negotiating the curve, the radius of curve is :-

A
$$\dfrac { 67.5 }{ 4 } m$$

B
45 m

C
54 m

D
30 m

Solution
Question 6
1 / -0

A mass is performing circular motion in a vertical plane centered at $$O$$. The average velocity of the particle is in creased, then at which point the string will break:

A
$$A$$

B
$$B$$

C
$$C$$

D
$$D$$

Solution
Question 7
1 / -0

A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown. Relative to its initial position with respect to the table, the ball
I. Remains stationary if there is no friction between the paper and the ball.
II. Moves to the left and starts rolling backwards, i.e. to the left if there is a friction between the paper and the ball.
III. Moves forward, i.e., in the direction in which the paper is pulled.
Here, the correct statements is/ are

A
I and II only

B
III only

C
I only

D
II only

Solution
Question 8
1 / -0

Force applied on a body is given by $$ F = (3t^2 - 2t + 10) N$$ where t is in seconds. Find impulse in t = 0 to t = 2 sec.

A
$$ 24 Kg ms^{-1} $$

B
$$ 2.4 Kg ms^{-1} $$

C
$$ 24 Kg^{-1} ms^{-1} $$

D
$$ 2.4 Kg^{-1} ms^{-1} $$

Solution
Question 9
1 / -0

A body of mass $$M$$ hits normally a rigid wall with velocity $$V$$ and bounces back with the same velocity. The impulse experienced by the body is

A
$$MV$$

B
$$1.5MV$$

C
$$2MV$$

D
zero

Solution

$$\textbf {Hint :}$$ Impulse is defined as the change in momentum in very small time.

$$\textbf{Step 1: Write initial and final momentum of body}$$
Let initially the body is moving along positive x- axis with speed $$v$$.
So, momentum of the body initially $$\vec{p_i} = mv \ \hat{i}$$
After bouncing back, the body moves along negative x-axis with same speed.
So, momentum of the body finally $$\vec{p_f} = -mv \ \hat{i}$$

$$\textbf{Step 2: Calculate impulse}$$
Thus change in momentum of body $$\Delta \vec{p} = \vec{p_f} - \vec{p_i} = -2mv \ \hat{i}$$
Impulse experienced $$\vec{I} = \Delta \vec{p} = -2mv \ \hat{i}$$
$$\implies \ |\vec{I}| = 2mv$$

$${\textbf{Correct option: C}}$$
Question 10
1 / -0

A cyclist riding the bicycle at a speed of $$ \sqrt { 3 } m/s $$ takes a turn around a circular road of radius $$ 20 \sqrt { 3 } m $$ without skidding. What is his inclination to the vertical?

A
$$ 30 $$

B
$$ 40 $$

C
$$ 60 $$

D
$$ 75 $$

Solution