Two wires of the same material (Young’s modulus \( Y \)) and same length \( L \) but radii \( R \) and \( 2R \) respectively, are joined end to end and a weight \( W \) is suspended from the combination. The elastic potential energy in the system is:
An ideal massless spring \( S \) can be compressed \( 1 \) m by a force of \( 100 \) N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at \( 30^\circ \) to the horizontal. A \( 10 \) kg block \( M \) is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by \( 2 \) m. If \( g = 10 \) m/s\( ^2 \), what is the speed of the mass just before it touches the spring?
A force of \( F = 0.5 \) N is applied on the lower block as shown in the figure. The work done by the lower block on the upper block for a displacement of 3 m of the upper block with respect to the ground is (Take, \( g = 10 \) m/s\( ^2 \)):
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of \( 60^\circ \) by a force of 10 N parallel to the inclined surface. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is:
[Given: \( g = 10 \) m/s\( ^2 \), \( \mu_s = 0.1 \)]
An object moves with speed \( v_1 \), \( v_2 \), and \( v_3 \) along a line segment \( AB \), \( BC \), and \( CD \) respectively as shown in the figure. Where \( AB = BC \) and \( AD = 3 AB \), then the average speed of the object will be: