Laws of Motion Test

Result

Laws of Motion Test - 54

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Question 1
1 / -0

The disc is at rest at the top of a rough inclined plane. It rolls without slipping. At the bottom of inclined plane there is a vertical groove if radius $$R$$. In order to loop the groove, the minimum height of incline required is:

A
$$\dfrac{15 R}{4}$$

B
$$\dfrac{9 R}{4}$$

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

D
$$\dfrac{7 R}{5}$$

Solution

Hence, option $$(A)$$ is correct answer.
Question 2
1 / -0

A rubber ball of mass 10 g falls from a height of $$80 cm$$ and rebounds to half of the original height. Impulse exerted by the ball on the floor is

A
0.068 N s

B
6.8 N s

C
0.0065 N s

D
0.68 N s

Solution
Question 3
1 / -0

If a car is to travel with a speed $$v$$ along the frictionless, banked circular track of radius $$r$$, the required angle of banking, so that the car does skids is ?

A
$$\theta=\tan^{-1}(\dfrac {v^{2}}{rg})$$

B
$$\theta=\tan^{-1}(\dfrac {v}{rg})$$

C
$$\theta=\tan^{-1}(\dfrac {r^{2}}{rg})$$

D
$$\theta < \tan^{-1}(\dfrac {v^{2}}{rg})$$

Solution
Question 4
1 / -0

A 10kg block is pullled along a frictionless surface in the form of an arc of a vertical circle of radius 10m, as shown in figure. The tangential applied force is 200 N. If the block started from rest at point P, then its velocity at Q will be (take $$g=10m/s^2$$)

A
$$15 m/s$$

B
$$16 m/s$$

C
$$20 m/s$$

D
$$18 m/s$$

Solution
Question 5
1 / -0

A player kicks a football of mass $$0.5$$kg and the football begins to move with a velocity of $$10 { m }/{ s }$$. If the contact between the leg and the football lasts for $$\dfrac { 1 }{ 50} $$ sec, then the force acted on the football should be

A
$$2500 N$$

B
$$1250 N$$

C
$$250 N$$

D
$$625 N$$

Solution

Momentum transferred to the ball is $$\Delta P=m\Delta v=0.5kg\times (10-0)=5Kgm/s$$
so the force will be $$F=\dfrac{\Delta p}{\Delta t}=\dfrac{5}{1/50}=250Kgm/s^2=250N$$
Question 6
1 / -0

A thin uniform rod of mass $$M$$ and length $$L$$ is hinged at its upper end released from rest in horizontal position. The tension at a point located at a point located at a point, when the rod becomes vertical, will be:

A
$$\dfrac {22Mg}{27} $$

B
$$\dfrac {11Mg}{13} $$

C
$$\dfrac {6Mg}{11} $$

D
$$2Mg$$

Solution

$$2mg$$

given,

$$0+mg \times 0=\dfrac{1}{2}Iw^2+mg\left ( -\dfrac{L}{2} \right )$$

$$\dfrac{1}{2}\left ( \dfrac{mL^2}{3} \right )w^2=\dfrac{mgL}{2}$$

$$w=\sqrt{\dfrac{3g}{L}}$$

$$T=mg+\dfrac{mv^2}{r}$$

$$=m[g+rw^2]$$

$$=m\left [ g+\dfrac{2L}{3} \times \dfrac{3g}{L} \right ]$$

$$=\dfrac{2m}{3} \times [g+2g]=2mg$$
Question 7
1 / -0

What is corrct statement about impulse?

A
change in velocity

B
change in momentum due to force in small time

C
change in acceleration

D
change in speed

Solution

Impulse:- It is defined as a change in momentum due to force in small time.
Mathematically,
From Newton's law,
$$F=\dfrac{\Delta p}{\Delta t}$$
Impulse, $$I=F\times \Delta t=\Delta P$$
The correct option is B.
Question 8
1 / -0

The coefficient of friction between the tyres and the road is $$0.25$$. The maximum speed with which a car can be driven around a curve of radius $$40m$$, without skidding is ? (assume $$g=10ms^{-2}$$)

A
$$40\ ms^{-1}$$

B
$$20\ ms^{-1}$$

C
$$15\ ms^{-1}$$

D
$$10\ ms^{-1}$$

Solution
Question 9
1 / -0

Safe maximum seed of the vehicle along an unbanked curved rough road of radius $$500m$$ and coefficient of static friction $$0.1$$ is

A
$$3.141m/s$$

B
$$11.2m/s$$

C
$$19m/s$$

D
$$22m/s$$

Solution
Question 10
1 / -0

A $$10$$ kkg object attached to a nylon cord outside a space vehicle is rotating at a speed of $$5 m/s$$. If the force acting on the cord is $$125 N$$ its radius of path is

A
2 m

B
4 m

C
6 m

D
1 m

Solution