Question

Assertion (A): When a solid Copper sphere and solid Wooden sphere, both having the same mass, are pinning about their own axis with same angular velocity, then the wooden sphere has greater angular momentum.
Reason (R): Wood is less denser than Copper. So radius of Wooden sphere is more than that of Copper and so greater moment of inertia.

• A. Both A and R are true and R is correct explanation of A
• B. Both A and R are true and R is not correct explanation of A
• C. A is true and R is false
• D. A is false and R is true

Answer 1

Answer: (A)

Both A and R are true and R is correct explanation of A

We know that

density of wood $\left(d_w\right)<$density of copper $\left(d_c\right)$

$d_w=\frac{m_w}{v_w}$

$d_v=\frac{m_c}{v_c}$

$m_c=m_w=m$

$\therefore v_w>v_c$

$\therefore R_w>R_c$

$w_w=w_c=w$

$L=Iw.$

$I_w=\frac{2}{5}m\left(R_w{)}^2\right),I_c=\frac{2}{5}m(R_c{)}^2$

$\therefore I_w>I_c(\because R_w>R_c)$

$L_w=I_{w}w,L_c=I_{c}w.$

$\therefore L_w>L_c(\because I_w>I_c)$