1
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ___________ m.

2
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1

A 0.5 kg block moving at a speed of 12 ms$$-$$1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _______________ Nm$$-$$1.

3
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $${h \over 2}$$. The spring constant is _____________ Nm$$-$$1.

(Use g = 10 ms$$-$$2)

4
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh$$-$$1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is ____________ $$\times$$ 105 N/m.