Wireless Sensor Network (WSN) is a self-structured network containing small, energy-constrained wireless nodes that act together to accomplish difficult tasks. Wearable sensors, one of the WSNs play a significant role in healthcare applications, especially patient monitoring. With a miniature size, wearable sensors have less space dedicated for energy sources. So it is important for wearable sensors to be manufactured as energy efficient and reliable and it must ensure quality of service in providing the data. Remote health care monitoring has two limitations such as adoption of mobility and the usage of low power consumption devices. To overcome these limitations, appropriate routing protocol can be used in Low Power Lossy Networks (LLNs). IPV6 Routing Protocol for Low Power Lossy Networks (RPL) is one of the routing protocols standardized to be applied in Internet of things network with wireless sensors. The current research article investigates the performance of RPL with three Objective Functions (OF), Minimum Rank with Hysteresis Objective Function (MRHOF) with Energy as metric, MRHOF with Expected Transmission count (ETX) as metrics and Objective Function zero(OF0) with hop count as metric, in elderly health care monitoring system. The study considered two scenarios case 1 has all static nodes while case 2 has few dynamic nodes. The performance was evaluated in terms of metrics control overhead, convergence time, Packet Delivery Ratio (PDR), Latency and energy consumption and the OF optimum for reliability, mobility and energy consumption is determined. The results of the simulation showed that, in mobile scenario OF0 converged at a fast rate than the MRHOF, which increases the life time. OF0 also consumed the least energy and it increased the life time of the node. As far as PDR is concerned, OF0 had low PDR when the nodes were mobile and ETX performed well.