Question

A conveyer belt of length l is moving with velocity v. A block of mass m is pushed against the motion of conveyer belt with velocity v₀ from end B with respect to conveyer belt. Co-efficient of friction between block and belt is µ. The value of v₀ so that the amount of heat liberated as a result of retardation of the block by conveyer belt is maximum is –

• A. $\sqrt { \mu \mathrm { g } \ell }$
• B. $\sqrt { 2 \mu \mathrm { g } \ell }$
• C. $2 \sqrt { \mu g \ell }$
• D. $\sqrt { 3 \mu \mathrm { g } \ell }$

Answer 1

Answer: (B)

$\sqrt { 2 \mu \mathrm { g } \ell }$

Answer 2

a = mg

v² = u² + 2as

0 = v₀² + 2 (– mg)l

v­₀ = $\sqrt { 2 \mu \mathrm { g } \ell }$