A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 $m / s$ at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be ______ J (given, coefficient of friction is 0.3 and g = 10 $m / s^{2}$ ). [2023]

Ans.
(54)

$a = - μ_{k} g = - 3$

$v = 18 - 3 \times 2$

$v = 12 m/s$

$K E = \frac{1}{2} m v^{2} + \frac{1}{2} (\frac{m r^{2}}{2}) \frac{v^{2}}{r^{2}}$

$K E = \frac{3}{4} m v^{2}$

$K E = 3 \times 18 = 54 J$

Want Us to Email you About Special Offers & Updates?