Magnitude using Vector: Derivation

Q.

A particle moves in a circle with a constant speed of 6m /s. Its centripetal acceleration is 120 m/s², The radius of the circle is

1. 300 cm

2. 200 cm

3. 20 cm

4. 30 cm

Q. in uniform circular motion as centripetal acceleration is not zero then how angular acceleration is zero

Q. An object moves on a circular path such that the distance covered is given by S = (0.5t2 + 2t) m, here t is time in s. If radius of circle is 4 m, then initial acceleration of object is

Q. Is angular acc. is different from centripetal acc. and why and what is this angular acc.

Q. A car of mass $m=1000\text{kg}$ is moving with constant speed $v=10\text{m/s}$ on a parabolic shaped bridge $AFOE$ of span $l=40\text{m}$ and height $h=20\text{m}$ as shown in the figure. Then the net force applied by the bridge on the car, when it is at point $F$ is :

Assume $g=10{\text{ms}}^{-2}$

1. $5000\sqrt{\frac{5}{2}}\text{N}$
2. $\frac{5000}{\sqrt{2}}\text{N}$
3. $\frac{10000}{\sqrt{2}}\text{N}$
4. $5000\sqrt{\frac{2}{5}}\text{N}$

Q.

A bead 'B' of mass m is attached to one end of a spring(AB) of natural length R and spring constant K= ($\sqrt{3}$+1)mg/R. The normal reaction at B just after it is released to move is:

1. 

2. mg

3. mg

4. mg

Q. A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5\text{m/s}$. What is the height of the plane of circle from vertex of the funnel?

1. $0.25\text{cm}$
2. $2\text{cm}$
3. $0.025\text{cm}$
4. $2.5\text{cm}$

Q. An object of $60\text{kg-wt}$ is weighed by hanging it to the spring balance, from the ceiling of a car. If the car starts moving around a curve of radius $10\text{m}$ at a speed $10{\text{ms}}^{-1}$. The reading of the spring balance would be
[$1\text{kg-wt}=10\text{N}$]

1. $60\sqrt{2}\text{kg-wt}$
2. $60\text{kg-wt}$
3. $120\sqrt{2}\text{kg-wt}$
4. $600\text{kg-wt}$

Q. a body makes uniform circular motion about a point in 2 dimension . but centripetal acceleration is not constant vector why​

Q. A chain of $125$ links is $1.25m$ long and has a mass of $2\text{kg}$. With the ends fastened together, it is set rotating at $3000\text{rpm}$. The centripetal force(in $\text{N}$) on each link is( consider $\pi =3.14$)

Q.

a ball rotating in a circular path of radius 2m makes 35 revolutions in 44sec. What will be the centripetal acceleration.

Q. Many accelerations act on a particle in circular motion, there is total acceleration from centripetal acceleration and tangential acceleration. But there is also angular acceleration. So why isnt it included in total acceleration?