TS EAMCET 4 May 2018 Shift 1 Solved Paper

Balance the force perpendicular to the inclined plane.
N=mg‌cos‌θ
Balance the force parallel to the inclined plane.
mg‌sin‌θ−fr=m

dv

dt

dv

dt

=

mg‌sin‌θ−fr

m

v(t)=∫g‌sin‌θ‌d‌t−

1

m

‌∫frdt
The expression to calculate the torque is given by,
τ=I

dω

dt

=r×Fr

dω

dt

=

rFr

mk2

ω(t)=

R2

mk2

‌∫frdt
Simplify further,

1

m

‌∫frdt=

k2

R

ω(t)
=

k2

R2

v(t)
The velocity is calculated as,
v(t)=∫g‌sin‌θ‌d‌t−

k2

R2

v(t)
=

1

(1+ k2 R2 )

‌∫g‌sin‌θ‌d‌t
The acceleration is calculated as,
a(t)=

dv(t)

dt

=

g‌sin‌θ

(1+ k2 R2 )