A small block is connected to one end of a massless spring of unstretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency to = (π /3) rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at / = 1 s, the value of v is (take g = 10 m /s2

Question

A small block is connected to one end of a massless spring of unstretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency to = (π /3) rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at / = 1 s, the value of v is (take g = 10 m /s2  (A) √50 m/s  (B) √51 m/s  (C) √52 m/s  (D) √53 m/s

Tardigrade Admin · Accepted Answer

t = time of flight of projectile = ( 2v sin θ / g ) (θ = 45 ° ) ∴ v= ( gt/ 2 sin θ = ( 10 × 1) 2 × 1/ √ 2) = √ 50 m/s

$50 m / s$

$51 m / s$

$52 m / s$

$53 m / s$

t = time of flight of projectile
$= \frac{2 v s in θ}{g} (θ = 4 5^{\circ})$
$∴ v = \frac{g t}{2 s in θ = \frac{10 \times 1}{2 \times 1/ 2}}$
$= 50 m / s$

50​m/s

51​m/s

52​m/s

53​m/s

t = time of flight of projectile =g2vsinθ​(θ=45∘) ∴v=2sinθ=2×1/2​10×1​gt​ =50​m/s

$50 m / s$

$51 m / s$

$52 m / s$

$53 m / s$

t = time of flight of projectile
$= \frac{2 v s in θ}{g} (θ = 4 5^{\circ})$
$∴ v = \frac{g t}{2 s in θ = \frac{10 \times 1}{2 \times 1/ 2}}$
$= 50 m / s$