Physics - NLM Question with Solution | TestHub

${\mathrm{a}}_{\mathrm{T}}=5\mathrm{m}/{\mathrm{s}}^2$ (Towards left)

considering left as positive and drawing FBD of block in frame of trolley:

$\mathrm{ma}-\mu \mathrm{mg}={\mathrm{ma}}_{\mathrm{B}/\mathrm{T}}$

$10-0.4\times 2\times 10=2\times {\mathrm{a}}_{\mathrm{B}/\mathrm{T}}$

${\mathrm{a}}_{\mathrm{B}/\mathrm{T}}=1\mathrm{m}/{\mathrm{s}}^2$ (Towards right)

${\mathrm{a}}_{\mathrm{B}/\mathrm{T}}={\mathrm{a}}_{\mathrm{B}}-{\mathrm{a}}_{\mathrm{T}}$

$\Rightarrow {\mathrm{a}}_{\mathrm{B}}={\mathrm{a}}_{\mathrm{B}/\mathrm{T}}+{\mathrm{a}}_{\mathrm{T}}$

$=-1+5$ ${\mathrm{a}}_{\mathrm{B}}=4\mathrm{m}/{\mathrm{s}}^2$

(Towards left) Thus, acceleration of block w.r.t ground is $4\mathrm{m}/{\mathrm{s}}^2$ towards left hence option (D) is correct.