A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of 30°. The external force required to take the same body up the plane with the same acceleration will be: (g = 10 m/s2)

Question

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of 30°. The external force required to take the same body up the plane with the same acceleration will be: (g = 10 m/s2) (A) 14 N (B) 20 N (C) 6 N (D) 4 N

Tardigrade Admin · Accepted Answer

Equation of motion when the mass slides down is

m g sin θ - f = ma

Given:

m = 2 k g; sin 3 0^{\circ} = \frac{1}{2}; g = 10 m / s; a = 3 m / s^{2}

Therefore, from Eq. (1), we have

f = m g sin θ - ma = 2 \times 10 \times \frac{1}{2} - 2 \times 3 = 4 N

Equation of motion when mass is pushed upward is

F - m g sin θ - f = ma

F = m g sin θ + ma + f = 2 \times 10 \times \frac{1}{2} + 2 \times 3 + 4

F = 10 + 6 + 4 = 20 N

Q. A body of mass 2kg slides down with an acceleration of 3m/s2 on a rough inclined plane having a slope of 30∘. The external force required to take the same body up the plane with the same acceleration will be : (g=10m/s2)

14 N

20 N

6 N

4 N

Equation of motion when the mass slides down is mgsinθ−f=ma Given: m=2kg;sin30∘=21​;g=10m/s;a=3m/s2 Therefore, from Eq. (1), we have f=mgsinθ−ma=2×10×21​−2×3=4N Equation of motion when mass is pushed upward is F−mgsinθ−f=ma F=mgsinθ+ma+f=2×10×21​+2×3+4 F=10+6+4=20N

Q. A body of mass $2 k g$ slides down with an acceleration of $3 m / s^{2}$ on a rough inclined plane having a slope of $3 0^{\circ}$ . The external force required to take the same body up the plane with the same acceleration will be : $(g = 10 m / s^{2})$