For an object in equilibrium, the net force acting on it must be zero.

Potential Energy = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.

Work done = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.

Work done = mgh = 4 kg × 9.8 m/s² × 3 m = 117.6 J.

Work done = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.

Centripetal force does no work as it acts perpendicular to the direction of motion.

The object has Kinetic Energy due to its motion in the circular path.

Centripetal force (F_c) = mv²/r = 2 kg * (5 m/s)² / (10 m) = 5 N.

Period (T) = 2πr/v = 2π(10)/5 = 4π s.

Linear speed (v) = rω = 3 m * 2 rad/s = 6 m/s.

Convex mirrors always produce virtual and erect images.

Using the lens formula 1/f = 1/v - 1/u, we find v = 20 cm.

For a concave lens, the image formed is virtual and erect when the object is placed in front of it.

Using the lens formula, the image is formed at 30 cm on the opposite side.

Using the lens formula 1/f = 1/v - 1/u, we find v = 33.33 cm.

Using the lens formula, 1/f = 1/v - 1/u, we find v = 30 cm, meaning the image is formed 30 cm on the opposite side.

Using the lens formula, 1/f = 1/v - 1/u. Here, f = 15 cm, u = -30 cm. Solving gives v = 10 cm.

Using the lens formula 1/f = 1/v - 1/u, we find v = 10 cm.

A concave lens always forms a virtual and erect image regardless of the object position.

When the object is at the focus of a concave mirror, the rays are parallel after reflection, resulting in no image being formed.

Horizontal component (v_x) = u * cos(θ) = 30 * (1/2) = 15 m/s.

Vertical component (v_y) = u * sin(θ) = 30 * (√3/2) = 25.98 m/s.

Horizontal component Vx = u * cos(θ) = 30 * (1/2) = 15 m/s.

Time of flight (T) = (2u * sin(θ)) / g = (2 * 30 * √3/2) / 9.8 = 5.18 s.

Time of flight (T) = (2 * u * sin(θ)) / g = (2 * 40 * 0.5) / 9.8 ≈ 4.08 s.

Time of flight (t) = √(2h/g) = √(2*45/9.8) = 3.03 s. Horizontal distance = speed * time = 10 * 3.03 = 30.3 m.

Time of flight (t) = √(2h/g) = √(2*45/9.8) = 3.03 s. Horizontal distance = speed * time = 10 * 3.03 = 30.3 m.

Using h = (1/2)gt^2, we have 80 = (1/2)(9.8)t^2, solving gives t ≈ 4 s.

Using h = (1/2)gt^2, we have 80 = (1/2)(9.8)t^2, solving gives t ≈ 4 s.

Using the equation h = (1/2)gt², where h = 80 m and g = 9.8 m/s², we have 80 = (1/2)*9.8*t². Solving gives t² = 16.33, so t ≈ 4 s.