Laws of Motion Test

Result

Laws of Motion Test - 61

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Question 1
1 / -0

At time $$t$$ second, a particle of mass $$3\ kg$$ has position vector $$\vec {r}$$ metre where $$\vec {r} = 3t\hat {i} - 4\cos t \hat {j}$$. The impulse of the force during the time interval $$0 < t < \dfrac {\pi}{2}$$ is

A
$$12\hat {j} N-s$$

B
$$9\hat {j} N-s$$

C
$$4\hat {j} N-s$$

D
$$14\hat {j} N-s$$

Solution
Question 2
1 / -0

A $$0.1\ kg$$ body moves at a constant speed of $$10\ m/s$$. It is pushed by applying a constant force for $$2\sec$$. Due to this force, it starts moving exactly in the opposite direction with a speed of $$4\ m/s$$. Then

A
The deceleration of the body is $$7\ m/s^{2}$$

B
The magnitude of change in momentum is $$1.4\ kg-m/\sec$$

C
Impulse of the force is $$1.4\ Ns$$

D
The force which acts on the ball is $$0.7\ N$$

E
All of the above

Solution
Question 3
1 / -0

Mark correct option or options.

A
The body of greater mass needs more forces to move due to more inertia

B
Force versus time graph gives impulse

C
Microscope area of contact is about $$10^{-4}$$ times actual area of the contact

D
All of the above

Solution
Question 4
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If a number of forces act on a body and the body is in static of dynamic equilibrium then

A
Work done by any individual force must be zero

B
Net work done by all the forces is positive

C
Net work done by all the forces is negative

D
Net work done by all the forces is zero

Solution
Question 5
1 / -0

A ring of mass $$5\ kg$$ sliding on a frictionless vertical rod is connected by a block $$B$$ of mass $$10\ kg$$ by the help of a massless string. Then at the equilibrium of the system the value of $$\theta$$ is

A
$$30^{\circ}$$

B
$$60^{\circ}$$

C
$$90^{\circ}$$

D
$$0^{\circ}$$

Solution
Question 6
1 / -0

In the figure, a block of weight $$60\ N$$ is placed on a rough surface. The coefficient of friction between the block and the surfaces is $$0.5$$. What minimum can be the weight $$W$$ such that the block does not slip on the surface?

A
$$60\ N$$

B
$$\dfrac{60}{\sqrt 2}N$$

C
$$30\ N$$

D
$$\dfrac{30}{\sqrt 2}N$$

Solution
Question 7
1 / -0

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

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

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

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

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

Solution

By conservation of linear momentum along the string
$$mu=(m+m+3m)v$$ or $$v=\dfrac{u}{5}$$
and impulse on block $$A=3m(v-0)=\dfrac{3mu}{5}$$.
Question 8
1 / -0

Consider the situation shown in the figure. The wall is smooth but the surfaces of $$A$$ and $$B$$ in contact are rough. Then

A
System may remain in equilibrium

B
Both bodies must move together

C
The system cannot remain in equilibrium

D
None of the above

Solution
Question 9
1 / -0

In the given figure, pulleys and strings are massless. For equilibrium of the system, the value of $$\alpha$$ is

A
$$60^{\circ}$$

B
$$30^{\circ}$$

C
$$90^{\circ}$$

D
$$120^{\circ}$$

Solution
Question 10
1 / -0

Consider the system as shown. The wall is smooth, but the surface of block A & B in contact is rough. the friction force on B due to A is equilibrium is:

A
Zero

B
Upwards

C
Downwards

D
The system can not remain in equilibrium

Solution