Two bodies of masses m1 and m2 are acted upon by equal forces F for equal time t. If the ratio of their masses is m1:m2 = 4:3, find the ratio of distances covered by them.

Step 1: Apply Newton's Second Law for both bodies. Given that the force F is equal for both bodies, and their masses are m_1 and m_2. According to Newton's Second Law, F = ma. For body 1: F = m_1 a_1 a_1 = (F)/(m_1) For body 2: F = m_2 a_2 a_2 = (F)/(m_2) Step 2: Use the equation of motion to find the distance covered. Both bodies start from rest (u=0) and act for equal time t. The equation for distance covered is s = ut + (1)/(2)at^2. Since u=0, the equation simplifies to s = (1)/(2)at^2. For body 1: s_1 = (1)/(2) a_1 t^2 = (1)/(2) ((F)/(m_1)) t^2 For body 2: s_2 = (1)/(2) a_2 t^2 = (1)/(2) ((F)/(m_2)) t^2 Step 3: Calculate the ratio of their distances covered. (s_1)/(s_2) = (1)/(2) ((F)/(m_1)) t^2(1)/(2) ((F)/(m_2)) t^2 = (1)/(m_1)(1)/(m_2) = (m_2)/(m_1) Given the ratio of their masses m_1:m_2 = 4:3. This means (m_1)/(m_2) = (4)/(3). Therefore, (m_2)/(m_1) = (3)/(4). So, the ratio of their distance covered is s_1:s_2 = 3:4. The correct option is (a). 11. (a) 3:4 Step 1: Find the velocity function by differentiating the displacement function. The displacement s is given by s = (1)/(3)t^3 + (1)/(2)t^2 - 12t + 5. Velocity v is the derivative of displacement with respect to time t: v = (ds)/(dt) = (d)/(dt)((1)/(3)t^3 + (1)/(2)t^2 - 12t + 5) v = (1)/(3)(3t^2) + (1)/(2)(2t) - 12(1) + 0 v = t^2 + t - 12 Step 2: Set the velocity to zero to find when the butterfly is momentarily at rest. When the butterfly is momentarily at rest, its velocity v=0. t^2 + t - 12 = 0 Step 3: Solve the quadratic equation for t. We can factor the quadratic equation: (t+4)(t-3) = 0 This gives two possible values for t: t+4 = 0 t = -4 s t-3 = 0 t = 3 s Since time cannot be negative, we take the positive value. The butterfly is momentarily at rest at t = 3 s. The correct option is (b). 12. (b) 3s That's 2 down. 3 left today — send the next one.