Question

A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10 π rad s⁻¹. Which of the two will start to roll earlier? The coefficient of kinetic friction is μk = 0.2.

Answer 1

It is given that Radii of the ring and the disc, r = 10 cm = 0.1 m
Initial angular speed, $\omega_0$ =10 π rad/s
Coefficient of kinetic friction, $\mu_k$ = 0.2
Initial velocity of both the objects, u = 0

Motion of the two objects is caused by frictional force.
From Newton’s 2nd law of motion,
we have, frictional force, f = ma
$\mu_kmg=ma$
a = Acceleration produced in the objects
m = Mass
∴ a = $\mu_kg$

Use formula, v = u + at
= 0 + $\mu_k$gt
= $\mu_k$gt.........(1)

The torque applied by the frictional force will act in perpendicularly outward direction and cause reduction in the initial angular speed.
Torque, τ= –Iα
Whrre, α is angular Acceleration
$\mu_k$mgr = –Iα
∴ α = –$\mu_k$mgr / I    

Use formula,  $\omega=\omega_0+\alpha t$
= ω0 + (–$\mu_k$mgr / I)t  

Rolling starts when linear velocity, v = rω
∴ v = r (ω0– μkmgrt / I)   .........(2)
Equating equations (1) and (2), we get:
$\mu_k$gt = r (ω0– $\mu_k$mgrt / I)
= rω0 – $\mu_k$mgr²t / I    ….(vi)
For the ring:
I = mr²
∴ μkgt = rω0 – μkmgr²t / mr²
= rω0 – μkgt
2μkgt = rω0
∴ t = rω0 / 2μkg
= 0.1 × 10 × 3.14 / 2 × 0.2 × 9.8  =  0.80 s   


For the disc: I = (1/2)mr2
∴ μkgt = rω0 – μkmgr2t / (1/2)mr2
= rω0 – 2μkgt
3μkgt = rω0
∴ t = rω0 / 3μkg
= 0.1 × 10 × 3.14 / 3 × 0.2 × 9.8  =  0.53 s 

Since td > tr, the disc will start rolling before the ring.

Answer 2

Answer:

1 answer · Physics 

 Best Answer

Pendulum period in seconds 

T ≈ 2π√(L/g) 

or, rearranging: 

g ≈ 4π²L/T² 

L ≈ T²g/4π² 

L is length of pendulum in meters 

g is gravitational acceleration = 9.8 m/s² 

The pendulum length is not mentioned, so I assume you have to calculate it from the above. 

period is 1 second. 

L ≈ (1)²g/4π² = 0.248 m. That size expanding to 1.1 meters doesn't make sense. 

I think you left part of the problem out, or copied it incorrectly. 

hope it helps

pls mark as brainliest

✨☺❤❤☺✨