Laws of Motion Test

Result

Laws of Motion Test - 72

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Question 1
1 / -0

A stone of mass 1 kg is tied to the end of a string of $$1m$$ length. It is whired in a vertical circel. If the velocity of the stone at the top be $$4m/s$$. What is the tension in the string (at that instant)?

A
$$6N$$

B
$$16N$$

C
$$5N$$

D
$$10N$$

Solution
Question 2
1 / -0

A stone of mass $$1kg$$ is tied to one end of a string of length $$0.5\ m$$. It is whirled in a veretical circular. If the maximum tension in the string is $$58.8N$$, the velocity at the top is

A
$$1.82\ ms^{-1}$$

B
$$2.2\ ms^{-1}$$

C
$$3.26\ ms^{-1}$$

D
$$2.87\ ms^{-1}$$

Solution
Question 3
1 / -0

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude & direction of acceleration of the stone:

A
$$\pi^2 \ m/s^2$$ and direction along the tangent to the circle.

B
$$\pi^2 \ m/s^2$$ and direction along the radius towards the centre.

C
$$\frac{\pi^2}{4} \ m/s^2$$ and direction along the radius towards the centre.

D
$$\pi^2 \ m/s^2$$ and direction along the radius away from the centre.

Solution
Question 4
1 / -0

Mass $$2m$$ is kept on a smooth circular track of mass $$m$$ , which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity $$\sqrt{2gR}$$ towards left and released. The maximum height reached by $$2m$$ will be ?

A
$$\dfrac {R}{4}$$

B
$$\dfrac {R}{2}$$

C
$$\dfrac {R}{3}$$

D
$$\dfrac {2R}{3}$$

Solution
Question 5
1 / -0

A stone is tied to a rope is rotated in a vertical circle with unifrom speed. if the difference between maximum and minimum tension in the rope is $$20N$$, mass of the stone in $$Kg$$ is $$(g=10m/s^{2})$$

A
$$0.75$$

B
$$1.0$$

C
$$1.5$$

D
$$0.5$$

Solution
Question 6
1 / -0

A ball of mass m strikes the fixed inclined plane inclined plane after falling through a height h. If it rebounds elastically, the impulse on the ball is:

A
$$2m\space cos\theta \sqrt(2gh)$$

B
$$2m\space cos\theta \sqrt(gh)$$

C
$$\dfrac{2m\sqrt(2gh)}{cos\theta} $$

D
$$2m \sqrt(2gh)$$

Solution

Refer image 1
Velocity by which it strikes the ground (v) is:
$$v^2-u^2=2gh$$
$$\Rightarrow v^2-0=2gh$$
$$\therefore v=\sqrt{2gh}$$
Refer image, 2
[As the collision is elastic ; the velocity of approval and velocity of separation along line of impact will be same]
As velocity of approach along Line of impact is $$\sqrt{2gh}\cos\theta$$ so velocity of separation will be $$-\sqrt{2gh}\cos\theta$$ [as it rebounds in the opposite direction]

$$\therefore P_i=m\times v_i=m\times \sqrt{2gh}\cos\theta$$

$$\therefore P_f=m\times v_f=-m\times \sqrt{2gh}\cos\theta$$

Now according to impulse - momentum theorem:
$$J=\Delta P$$
$$\Rightarrow J=m\times \sqrt{2gh}\cos\theta-(-m\times \sqrt{2gh}\cos\theta)$$
$$\Rightarrow J=2m\cos\theta\sqrt{2gh}$$

So the impulse on the ball is $$2m\cos\theta\sqrt{2gh}$$
Question 7
1 / -0

Two balls of the same mass are dropped from the same height h, on to the floor. The first ball bounces to a height $$h/4$$, after the collision & the second ball to a height $$h/16$$. The impulse applied by the first & second ball on the floor are $$I_1$$ and $$I_2$$ respectively. Then

A
$$5{I_1} = 6{I_2}$$

B
$$6{I_1} = 5{I_2}$$

C
$${I_1} = 2{I_2}$$

D
$$2{I_1} = {I_2}$$

Solution
Question 8
1 / -0

A system of two blocks $$A$$ and $$B$$ are connected by an inextensible massless strings as shown. The pulley is massless and frictionless. Initially the system is at rest when, a bullet of mass $$m$$ moving with a velocity $$u$$ as shown hits the block $$B$$ and gets embedded into it. The impulse imparted by tension force to the block of mass $$3m$$ is:

A
$$\cfrac{5mu}{4}$$

B
$$\cfrac{4mu}{5}$$

C
$$\cfrac{2mu}{5}$$

D
$$\cfrac{3mu}{5}$$

Solution
Question 9
1 / -0

Select the incorrect option:-
($$\tau = torque, \,v = velocity, \,\omega = angular \,velocity, \, a_c = centripetal \, acceleration$$)

A
$$\vec \tau \times \vec \tau = 0$$

B
$$\vec v . \vec \omega = 0$$

C
$$ \vec \omega \times \vec v= 0$$

D
$$ \vec a_c \times \vec v= 0$$

Solution
Question 10
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A road is banked at an angle of $$30^{o}$$ to the horizontal for negotiating a circular road of radius $$10 m$$. At what velocity a car will experience no friction while negotiating the curve?

A
$$54\ km/hr$$

B
$$72\ km/hr$$

C
$$27.36\ km/hr$$

D
$$28\ km/hr$$

Solution